{"author":"Prof. Dr. Tobias Lamm","courses":{"1":{"dir":"a1","title":"Analysis I","short":"Ana I","term":"WS 24/25","chapters":{"I":"Die reellen Zahlen","II":"Die vollständige Induktion","III":"Folgen und Grenzwerte","IV":"Teilmengen von R und Rⁿ","V":"Reihen","VI":"Stetigkeit und Grenzwerte von Funktionen","VII":"Der Zwischenwertsatz und Anwendungen","VIII":"Differentialrechnung","IX":"Konvergenz von Funktionenfolgen","X":"Das Riemannsche Integral","XI":"Ableitung und Integral"},"row":0},"2":{"dir":"a2","title":"Analysis II","short":"Ana II","term":"SS 25","chapters":{"I":"Metrische Räume","II":"Differentiation im Rⁿ","III":"Anwendungen der Differentialrechnung","IV":"Lokale Auflösung von Gleichungen","V":"Kurven und Kurvenintegrale","VI":"Gewöhnliche Differentialgleichungen"},"row":1},"3":{"dir":"a3","title":"Analysis III","short":"Ana III","term":"WS 25/26","chapters":{"I":"Maße und messbare Funktionen","II":"Äußere Maße","III":"Das Lebesgue-Maß","IV":"Lebesgue-Integral","V":"Konvergenzsätze und Lp-Räume","VI":"Satz von Fubini","VII":"Der Transformationssatz","VIII":"Das Flächenmaß auf Untermannigfaltigkeiten","IX":"Der Integralsatz von Gauß","X":"Faltung und Fouriertransformation"},"row":2},"L":{"dir":"la","title":"Lineare Algebra","short":"LA","term":"Leuzinger","format":"decimal","top_cut":88,"chapters":{"3":"Was ist lineare Algebra?","4":"Logik und Mengenlehre","5":"Algebraische Grundbegriffe","6":"Vektorräume: Definition und Beispiele","7":"Basis und Dimension","8":"Untervektorräume","9":"Lineare Abbildungen","10":"Abbildungsmatrizen","11":"Lineare Gleichungssysteme","12":"Determinanten","13":"Eigenwerte und Eigenvektoren","14":"Diagonalisierbare Endomorphismen","15":"Trigonalisierbare Endomorphismen","16":"Satz von Cayley-Hamilton","17":"Jordansche Normalform","18":"Euklidische und unitäre Vektorräume","19":"Homomorphismen mit Skalarprodukt","20":"Bilinearformen","21":"Affine und euklidische Geometrie"},"row":0}},"nodes":[{"id":"1:VOR","label":"VOR","course":"1","kind":"Basis","chapter":"0","name":null,"page":null,"title":"Logik, Mengen, ℕ, ℤ, ℚ","note":null,"deps":[],"links":[],"implied":[],"depth":0,"weight":799,"pos":[1936.3,290,30],"landmark":false,"img":{}},{"id":"1:K1","label":"K1","course":"1","kind":"Axiom","chapter":"I","name":null,"page":3,"title":"Assoziativgesetz (+)","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1315.9,677.9,28.2],"landmark":false,"img":{"s":[983,105]}},{"id":"1:K2","label":"K2","course":"1","kind":"Axiom","chapter":"I","name":null,"page":3,"title":"Kommutativgesetz (+)","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1537.6,602.5,28.2],"landmark":false,"img":{"s":[983,104]}},{"id":"1:K3","label":"K3","course":"1","kind":"Axiom","chapter":"I","name":null,"page":3,"title":"Neutrales Element 0","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1619.6,635.8,28.2],"landmark":false,"img":{"s":[983,105]}},{"id":"1:K4","label":"K4","course":"1","kind":"Axiom","chapter":"I","name":null,"page":4,"title":"Additives Inverses","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1385.7,623.6,28.2],"landmark":false,"img":{"s":[983,105]}},{"id":"1:K5","label":"K5","course":"1","kind":"Axiom","chapter":"I","name":null,"page":4,"title":"Assoziativgesetz (·)","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1467.7,656.9,28.2],"landmark":false,"img":{"s":[983,104]}},{"id":"1:K6","label":"K6","course":"1","kind":"Axiom","chapter":"I","name":null,"page":4,"title":"Kommutativgesetz (·)","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1549.7,690.1,28.2],"landmark":false,"img":{"s":[983,105]}},{"id":"1:K7","label":"K7","course":"1","kind":"Axiom","chapter":"I","name":null,"page":4,"title":"Neutrales Element 1","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1303.7,590.3,28.2],"landmark":false,"img":{"s":[983,104]}},{"id":"1:K8","label":"K8","course":"1","kind":"Axiom","chapter":"I","name":null,"page":4,"title":"Multiplikatives Inverses","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1397.9,711.2,28.2],"landmark":false,"img":{"s":[983,104]}},{"id":"1:K9","label":"K9","course":"1","kind":"Axiom","chapter":"I","name":null,"page":4,"title":"Distributivgesetz","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":580,"pos":[1455.6,569.2,28.2],"landmark":false,"img":{"s":[983,104]}},{"id":"1:O1","label":"O1","course":"1","kind":"Axiom","chapter":"I","name":null,"page":7,"title":"Trichotomie","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":573,"pos":[1233.9,644.7,28.2],"landmark":false,"img":{"s":[983,104]}},{"id":"1:O2","label":"O2","course":"1","kind":"Axiom","chapter":"I","name":null,"page":7,"title":"Verträglichkeit von > mit + und ·","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":573,"pos":[1373.6,535.9,28.2],"landmark":false,"img":{"s":[983,36]}},{"id":"1:I.14","label":"I.14","course":"1","kind":"Satz","chapter":"I","name":null,"page":11,"title":"x² = 2 ist in ℚ nicht lösbar","note":"Teilbarkeit in ℤ vorausgesetzt","deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":1,"pos":[1255.6,708.8,7.5],"landmark":false,"img":{"s":[983,42],"p":[983,810]}},{"id":"1:II.1","label":"II.1","course":"1","kind":"Axiom","chapter":"II","name":"Induktionsaxiom","page":15,"title":"Induktionsaxiom","note":"Axiom","deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":411,"pos":[2572.2,625.8,28.2],"landmark":false,"img":{"s":[983,280]}},{"id":"1:II.10","label":"II.10","course":"1","kind":"Definition","chapter":"II","name":null,"page":18,"title":"Fakultät","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":42,"pos":[2648.1,625.8,15.7],"landmark":false,"img":{"s":[983,188]}},{"id":"L:4.13","label":"4.13","course":"L","kind":"Definition","chapter":"4","name":null,"page":32,"title":"Abbildung, Bild, Urbild, Graph","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":705,"pos":[6500.4,303.1,28.2],"landmark":true,"img":{"s":[983,494]}},{"id":"L:4.18","label":"4.18","course":"L","kind":"Definition","chapter":"4","name":null,"page":34,"title":"Relation","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":27,"pos":[6568.4,273.8,13.8],"landmark":false,"img":{"s":[983,114]}},{"id":"L:5.64","label":"5.64","course":"L","kind":"Definition","chapter":"5","name":null,"page":65,"title":"Teilbarkeit","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":4,"pos":[5179.3,640.6,9],"landmark":false,"img":{"s":[983,296]}},{"id":"L:18.19","label":"18.19","course":"L","kind":"Definition","chapter":"18","name":null,"page":198,"title":"Metrik","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":11,"pos":[7124.5,1270.1,11],"landmark":false,"img":{"s":[983,337]}},{"id":"3:I.1","label":"I.1","course":"3","kind":"Definition","chapter":"I","name":null,"page":3,"title":"σ-Algebra, messbarer Raum","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":115,"pos":[3050.9,7314,22.1],"landmark":false,"img":{"s":[983,528]}},{"id":"3:II.9","label":"II.9","course":"3","kind":"Definition","chapter":"II","name":null,"page":22,"title":"∪-, ∩-, \\-stabile Mengensysteme","note":null,"deps":["1:VOR"],"links":["1:VOR"],"implied":[],"depth":1,"weight":64,"pos":[4374.1,7391.3,18],"landmark":false,"img":{"s":[983,159]}},{"id":"1:I.1","label":"I.1","course":"1","kind":"Definition","chapter":"I","name":"Körper","page":3,"title":"Körper","note":null,"deps":["1:K1","1:K2","1:K3","1:K4","1:K5","1:K6","1:K7","1:K8","1:K9"],"links":["1:K1","1:K2","1:K3","1:K4","1:K5","1:K6","1:K7","1:K8","1:K9"],"implied":[],"depth":2,"weight":579,"pos":[1479.9,744.5,28.2],"landmark":false,"img":{"s":[983,1939]}},{"id":"1:II.3","label":"II.3","course":"1","kind":"Satz","chapter":"II","name":"Vollständige Induktion","page":16,"title":"Vollständige Induktion","note":null,"deps":["1:II.1"],"links":["1:II.1"],"implied":[],"depth":2,"weight":409,"pos":[2588.1,778.8,28.2],"landmark":true,"img":{"s":[983,251],"p":[983,658]}},{"id":"1:II.12","label":"II.12","course":"1","kind":"Definition","chapter":"II","name":"Binomialkoeffizienten","page":19,"title":"Binomialkoeffizienten","note":null,"deps":["1:II.10"],"links":["1:II.10"],"implied":[],"depth":2,"weight":40,"pos":[2548.9,709.8,15.5],"landmark":false,"img":{"s":[983,316]}},{"id":"1:II.7","label":"II.7","course":"1","kind":"Definition","chapter":"II","name":null,"page":17,"title":"Injektiv, surjektiv, bijektiv","note":null,"deps":["1:VOR","L:4.13"],"links":["L:4.13"],"implied":[{"id":"1:VOR","via":"L:4.13"}],"depth":2,"weight":512,"pos":[2623.7,697.7,28.2],"landmark":false,"img":{"s":[983,244]}},{"id":"L:4.15","label":"4.15","course":"L","kind":"Definition","chapter":"4","name":null,"page":33,"title":"Injektiv, surjektiv, bijektiv","note":null,"deps":["L:4.13"],"links":["L:4.13"],"implied":[],"depth":2,"weight":106,"pos":[6470.2,379,21.4],"landmark":false,"img":{"s":[983,1311]}},{"id":"L:4.16","label":"4.16","course":"L","kind":"Definition","chapter":"4","name":null,"page":34,"title":"Gleichheit, Einschränkung, Verkettung von Abbildungen","note":null,"deps":["L:4.13"],"links":["L:4.13"],"implied":[],"depth":2,"weight":106,"pos":[6595.4,336.9,21.4],"landmark":false,"img":{"s":[983,673]}},{"id":"L:5.1","label":"5.1","course":"L","kind":"Definition","chapter":"5","name":null,"page":40,"title":"Verknüpfung","note":null,"deps":["L:4.13"],"links":["L:4.13"],"implied":[],"depth":2,"weight":557,"pos":[5241,680,28.2],"landmark":false,"img":{"s":[983,101]}},{"id":"L:4.20","label":"4.20","course":"L","kind":"Definition","chapter":"4","name":null,"page":35,"title":"Ordnungsrelation","note":null,"deps":["L:4.18"],"links":["L:4.18"],"implied":[],"depth":2,"weight":1,"pos":[6437.3,327.7,7.5],"landmark":false,"img":{"s":[983,370]}},{"id":"L:4.22","label":"4.22","course":"L","kind":"Definition","chapter":"4","name":null,"page":35,"title":"Äquivalenzrelation","note":null,"deps":["L:4.18"],"links":["L:4.18"],"implied":[],"depth":2,"weight":24,"pos":[6536,367.5,13.3],"landmark":false,"img":{"s":[983,276]}},{"id":"L:5.65","label":"5.65","course":"L","kind":"Definition","chapter":"5","name":null,"page":65,"title":"Größter gemeinsamer Teiler","note":null,"deps":["L:5.64"],"links":["L:5.64"],"implied":[],"depth":2,"weight":3,"pos":[5162.2,698.5,8.6],"landmark":false,"img":{"s":[983,256]}},{"id":"L:18.43","label":"18.43","course":"L","kind":"Definition","chapter":"18","name":null,"page":210,"title":"Abstand von Mengen","note":null,"deps":["L:18.19"],"links":["L:18.19"],"implied":[],"depth":2,"weight":1,"pos":[7110.9,1333.9,7.5],"landmark":false,"img":{"s":[983,455]}},{"id":"L:19.16","label":"19.16","course":"L","kind":"Definition","chapter":"19","name":null,"page":227,"title":"Isometrie metrischer Räume","note":null,"deps":["L:18.19"],"links":["L:18.19"],"implied":[],"depth":2,"weight":7,"pos":[7085.3,1867.9,10],"landmark":false,"img":{"s":[983,285]}},{"id":"3:I.2","label":"I.2","course":"3","kind":"Satz","chapter":"I","name":null,"page":3,"title":"Durchschnitte von σ-Algebren","note":null,"deps":["3:I.1"],"links":["3:I.1"],"implied":[],"depth":2,"weight":75,"pos":[3009.6,7374.3,19],"landmark":false,"img":{"s":[983,61],"p":[983,99]}},{"id":"3:I.11","label":"I.11","course":"3","kind":"Definition","chapter":"I","name":null,"page":9,"title":"Messbare Abbildung","note":null,"deps":["3:I.1"],"links":["3:I.1"],"implied":[],"depth":2,"weight":53,"pos":[3121,7325.1,16.9],"landmark":false,"img":{"s":[983,681]}},{"id":"3:II.10","label":"II.10","course":"3","kind":"Definition","chapter":"II","name":null,"page":22,"title":"Ring, Algebra","note":null,"deps":["3:II.9"],"links":["3:II.9"],"implied":[],"depth":2,"weight":59,"pos":[4398.1,7454.4,17.5],"landmark":false,"img":{"s":[983,432]}},{"id":"3:II.19","label":"II.19","course":"3","kind":"Definition","chapter":"II","name":null,"page":27,"title":"Halbring","note":null,"deps":["3:II.9"],"links":["3:II.9"],"implied":[],"depth":2,"weight":54,"pos":[4528.1,7459.2,17],"landmark":false,"img":{"s":[983,376]}},{"id":"1:I.2","label":"I.2","course":"1","kind":"Lemma","chapter":"I","name":"Eindeutigkeit der neutralen Elemente","page":4,"title":"Eindeutigkeit der neutralen Elemente","note":null,"deps":["1:I.1","1:K2","1:K3","1:K6","1:K7"],"links":["1:I.1"],"implied":[{"id":"1:K2","via":"1:I.1"},{"id":"1:K3","via":"1:I.1"},{"id":"1:K6","via":"1:I.1"},{"id":"1:K7","via":"1:I.1"}],"depth":3,"weight":0,"pos":[1475.3,810.6,6],"landmark":false,"img":{"s":[983,260],"p":[983,285]}},{"id":"1:I.3","label":"I.3","course":"1","kind":"Lemma","chapter":"I","name":"Kürzungsregeln","page":5,"title":"Kürzungsregeln","note":null,"deps":["1:I.1","1:K1","1:K3","1:K4","1:K5","1:K7","1:K8"],"links":["1:I.1"],"implied":[{"id":"1:K1","via":"1:I.1"},{"id":"1:K3","via":"1:I.1"},{"id":"1:K4","via":"1:I.1"},{"id":"1:K5","via":"1:I.1"},{"id":"1:K7","via":"1:I.1"},{"id":"1:K8","via":"1:I.1"}],"depth":3,"weight":500,"pos":[1328.1,765.6,28.2],"landmark":false,"img":{"s":[983,111],"p":[983,342]}},{"id":"1:I.7","label":"I.7","course":"1","kind":"Definition","chapter":"I","name":null,"page":7,"title":"Angeordneter Körper","note":null,"deps":["1:I.1","1:O1","1:O2"],"links":["1:I.1","1:O1","1:O2"],"implied":[],"depth":3,"weight":572,"pos":[1410.1,798.9,28.2],"landmark":false,"img":{"s":[983,405]}},{"id":"1:II.4","label":"II.4","course":"1","kind":"Satz","chapter":"II","name":"Arithmetische Summenformel","page":16,"title":"Arithmetische Summenformel","note":null,"deps":["1:II.3"],"links":["1:II.3"],"implied":[],"depth":3,"weight":0,"pos":[2686.4,719.3,6],"landmark":false,"img":{"s":[983,135],"p":[983,352]}},{"id":"1:II.13","label":"II.13","course":"1","kind":"Lemma","chapter":"II","name":null,"page":19,"title":"Rekursion der Binomialkoeffizienten","note":null,"deps":["1:II.12"],"links":["1:II.12"],"implied":[],"depth":3,"weight":39,"pos":[2514.3,762.3,15.4],"landmark":false,"img":{"s":[983,129],"p":[983,572]}},{"id":"1:II.8","label":"II.8","course":"1","kind":"Satz","chapter":"II","name":"Schubfachprinzip","page":18,"title":"Schubfachprinzip","note":null,"deps":["1:II.7","1:II.3"],"links":["1:II.7","1:II.3"],"implied":[],"depth":3,"weight":303,"pos":[2676.4,784.8,28.2],"landmark":false,"img":{"s":[983,74],"p":[983,658]}},{"id":"1:IV.1","label":"IV.1","course":"1","kind":"Definition","chapter":"IV","name":null,"page":40,"title":"Gleichmächtigkeit","note":null,"deps":["1:II.7"],"links":["1:II.7"],"implied":[],"depth":3,"weight":4,"pos":[804.8,1696.7,9],"landmark":false,"img":{"s":[983,129]}},{"id":"L:4.17","label":"4.17","course":"L","kind":"Lemma","chapter":"4","name":null,"page":34,"title":"Verkettung ist assoziativ","note":null,"deps":["L:4.16"],"links":["L:4.16"],"implied":[],"depth":3,"weight":105,"pos":[6522.2,432.8,21.4],"landmark":false,"img":{"s":[983,68],"p":[983,291]}},{"id":"L:5.4","label":"5.4","course":"L","kind":"Definition","chapter":"5","name":null,"page":40,"title":"Assoziativ, kommutativ","note":null,"deps":["L:5.1"],"links":["L:5.1"],"implied":[],"depth":3,"weight":555,"pos":[5109.6,751.8,28.2],"landmark":false,"img":{"s":[983,264]}},{"id":"L:5.6","label":"5.6","course":"L","kind":"Definition","chapter":"5","name":null,"page":42,"title":"Neutrales und inverses Element","note":null,"deps":["L:5.1"],"links":["L:5.1"],"implied":[],"depth":3,"weight":555,"pos":[5198,757.3,28.2],"landmark":false,"img":{"s":[983,321]}},{"id":"L:4.24","label":"4.24","course":"L","kind":"Satz","chapter":"4","name":"Äquivalenzklassen-Zerlegung","page":36,"title":"Zerlegung in Äquivalenzklassen","note":null,"deps":["L:4.22"],"links":["L:4.22"],"implied":[],"depth":3,"weight":20,"pos":[6457.1,443.8,12.7],"landmark":false,"img":{"s":[983,69],"p":[983,4370]}},{"id":"L:5.67","label":"5.67","course":"L","kind":"Lemma","chapter":"5","name":null,"page":66,"title":"Euklidischer Algorithmus liefert den ggT","note":null,"deps":["L:5.65"],"links":["L:5.65"],"implied":[],"depth":3,"weight":2,"pos":[5265,744,8.1],"landmark":false,"img":{"s":[983,36]}},{"id":"L:21.31","label":"21.31","course":"L","kind":"Definition","chapter":"21","name":null,"page":272,"title":"Euklidische Isometrie (Bewegung)","note":null,"deps":["L:18.19","L:19.16"],"links":["L:19.16"],"implied":[{"id":"L:18.19","via":"L:19.16"}],"depth":3,"weight":6,"pos":[7158.1,1320.3,9.7],"landmark":false,"img":{"s":[983,131]}},{"id":"3:I.3","label":"I.3","course":"3","kind":"Definition","chapter":"I","name":null,"page":3,"title":"Erzeugte σ-Algebra","note":null,"deps":["3:I.2"],"links":["3:I.2"],"implied":[],"depth":3,"weight":74,"pos":[3170.4,7451.2,18.9],"landmark":false,"img":{"s":[983,1152]}},{"id":"3:II.20","label":"II.20","course":"3","kind":"Satz","chapter":"II","name":null,"page":27,"title":"Die Intervalle bilden einen Halbring","note":null,"deps":["3:II.19"],"links":["3:II.19"],"implied":[],"depth":3,"weight":43,"pos":[4357.3,7508.2,15.8],"landmark":false,"img":{"s":[983,42],"p":[983,356]}},{"id":"3:II.21","label":"II.21","course":"3","kind":"Satz","chapter":"II","name":null,"page":27,"title":"Produkte von Halbringen","note":null,"deps":["3:II.19"],"links":["3:II.19"],"implied":[],"depth":3,"weight":43,"pos":[4486,7525.9,15.8],"landmark":false,"img":{"s":[983,70],"p":[983,653]}},{"id":"3:II.23","label":"II.23","course":"3","kind":"Satz","chapter":"II","name":null,"page":28,"title":"Von einem Halbring erzeugter Ring","note":null,"deps":["3:II.19","3:II.10"],"links":["3:II.19","3:II.10"],"implied":[],"depth":3,"weight":47,"pos":[4550,7529.4,16.3],"landmark":false,"img":{"s":[983,72],"p":[983,614]}},{"id":"1:I.4","label":"I.4","course":"1","kind":"Lemma","chapter":"I","name":"Eindeutigkeit der inversen Elemente","page":5,"title":"Eindeutigkeit der Inversen","note":null,"deps":["1:I.1","1:K2","1:K4","1:K6","1:K8","1:I.3"],"links":["1:I.3"],"implied":[{"id":"1:I.1","via":"1:I.3"},{"id":"1:K2","via":"1:I.1"},{"id":"1:K4","via":"1:I.1"},{"id":"1:K6","via":"1:I.1"},{"id":"1:K8","via":"1:I.1"}],"depth":4,"weight":499,"pos":[1340.3,853.3,28.2],"landmark":false,"img":{"s":[983,277],"p":[983,336]}},{"id":"1:I.9","label":"I.9","course":"1","kind":"Definition","chapter":"I","name":null,"page":8,"title":"Betrag","note":null,"deps":["1:I.7"],"links":["1:I.7"],"implied":[],"depth":4,"weight":505,"pos":[1456.6,874.2,28.2],"landmark":false,"img":{"s":[983,216]}},{"id":"1:I.11","label":"I.11","course":"1","kind":"Definition","chapter":"I","name":null,"page":9,"title":"Schranken, Supremum, Infimum","note":null,"deps":["1:I.7"],"links":["1:I.7"],"implied":[],"depth":4,"weight":559,"pos":[1537.3,834,28.2],"landmark":false,"img":{"s":[983,1268]}},{"id":"1:II.15","label":"II.15","course":"1","kind":"Satz","chapter":"II","name":"Binomischer Lehrsatz","page":20,"title":"Binomischer Lehrsatz","note":null,"deps":["1:II.13","1:II.12","1:II.3"],"links":["1:II.13","1:II.3"],"implied":[{"id":"1:II.12","via":"1:II.13"}],"depth":4,"weight":37,"pos":[2524.3,926.9,15.1],"landmark":false,"img":{"s":[983,137],"p":[983,543]}},{"id":"1:II.9","label":"II.9","course":"1","kind":"Definition","chapter":"II","name":null,"page":18,"title":"Endliche Mengen, Anzahl","note":null,"deps":["1:II.7","1:II.8"],"links":["1:II.8"],"implied":[{"id":"1:II.7","via":"1:II.8"}],"depth":4,"weight":302,"pos":[2566.9,864.7,28.2],"landmark":false,"img":{"s":[983,419]}},{"id":"1:IV.2","label":"IV.2","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":40,"title":"Gleichmächtigkeit ist Äquivalenzrelation","note":null,"deps":["1:IV.1","1:II.7","L:4.22"],"links":["1:IV.1","L:4.22"],"implied":[{"id":"1:II.7","via":"1:IV.1"}],"depth":4,"weight":0,"pos":[813.9,1756.9,6],"landmark":false,"img":{"s":[983,243],"p":[983,319]}},{"id":"L:5.9","label":"5.9","course":"L","kind":"Definition","chapter":"5","name":null,"page":42,"title":"Gruppe","note":null,"deps":["L:5.4","L:5.6"],"links":["L:5.4","L:5.6"],"implied":[],"depth":4,"weight":554,"pos":[5267.3,812.3,28.2],"landmark":true,"img":{"s":[983,401]}},{"id":"L:5.69","label":"5.69","course":"L","kind":"Lemma","chapter":"5","name":"Lemma von Bézout","page":66,"title":"Lemma von Bézout","note":null,"deps":["L:5.67"],"links":["L:5.67"],"implied":[],"depth":4,"weight":1,"pos":[5335,813.7,7.5],"landmark":false,"img":{"s":[983,100],"p":[983,771]}},{"id":"3:I.12","label":"I.12","course":"3","kind":"Lemma","chapter":"I","name":null,"page":9,"title":"Messbarkeit über Erzeuger prüfen","note":"Benutzt Übungsblatt 1","deps":["3:I.11","3:I.3"],"links":["3:I.11","3:I.3"],"implied":[],"depth":4,"weight":52,"pos":[2994.3,7495.5,16.8],"landmark":false,"img":{"s":[983,70],"p":[983,751]}},{"id":"3:II.22","label":"II.22","course":"3","kind":"Satz","chapter":"II","name":null,"page":28,"title":"Die Quader bilden einen Halbring","note":"Kein eigener Beweis: folgt aus II.20, II.21","deps":["3:II.20","3:II.21"],"links":["3:II.20","3:II.21"],"implied":[],"depth":4,"weight":42,"pos":[4384.8,7570.1,15.7],"landmark":false,"img":{"s":[983,42]}},{"id":"3:II.24","label":"II.24","course":"3","kind":"Lemma","chapter":"II","name":null,"page":28,"title":"σ(Halbring) = σ(erzeugter Ring)","note":null,"deps":["3:II.23","3:I.3"],"links":["3:II.23","3:I.3"],"implied":[],"depth":4,"weight":37,"pos":[4447.4,7575.7,15.1],"landmark":false,"img":{"s":[983,169],"p":[983,70]}},{"id":"3:II.25","label":"II.25","course":"3","kind":"Lemma","chapter":"II","name":null,"page":29,"title":"Disjunkte Zerlegung im erzeugten Ring","note":null,"deps":["3:II.23"],"links":["3:II.23"],"implied":[],"depth":4,"weight":45,"pos":[4321.6,7561.3,16.1],"landmark":false,"img":{"s":[983,71],"p":[983,487]}},{"id":"1:I.5","label":"I.5","course":"1","kind":"Definition","chapter":"I","name":null,"page":6,"title":"Notation −x und x⁻¹","note":null,"deps":["1:I.4"],"links":["1:I.4"],"implied":[],"depth":5,"weight":498,"pos":[1530.9,922.3,28.2],"landmark":false,"img":{"s":[983,274]}},{"id":"1:III.3","label":"III.3","course":"1","kind":"Definition","chapter":"III","name":null,"page":23,"title":"ε-Umgebung","note":null,"deps":["1:I.9"],"links":["1:I.9"],"implied":[],"depth":5,"weight":230,"pos":[1961.1,1413.6,28.2],"landmark":false,"img":{"s":[983,108]}},{"id":"1:I.12","label":"I.12","course":"1","kind":"Axiom","chapter":"I","name":"Vollständigkeitsaxiom","page":10,"title":"Vollständigkeitsaxiom","note":"Axiom","deps":["1:I.11"],"links":["1:I.11"],"implied":[],"depth":5,"weight":554,"pos":[1285.8,923,28.2],"landmark":true,"img":{"s":[983,166]}},{"id":"1:I.17","label":"I.17","course":"1","kind":"Lemma","chapter":"I","name":null,"page":13,"title":"Charakterisierung von sup und inf","note":null,"deps":["1:I.11"],"links":["1:I.11"],"implied":[],"depth":5,"weight":484,"pos":[1453.7,965.6,28.2],"landmark":false,"img":{"s":[983,159],"p":[983,186]}},{"id":"1:II.2","label":"II.2","course":"1","kind":"Satz","chapter":"II","name":null,"page":15,"title":"Wohlordnung von ℕ","note":null,"deps":["1:II.1","1:I.11"],"links":["1:II.1","1:I.11"],"implied":[],"depth":5,"weight":2,"pos":[2499.7,877.4,8.1],"landmark":false,"img":{"s":[983,75],"p":[983,764]}},{"id":"1:II.11","label":"II.11","course":"1","kind":"Satz","chapter":"II","name":"Permutationen","page":19,"title":"Anzahl der Permutationen","note":null,"deps":["1:II.3","1:II.10","1:II.9","1:II.7"],"links":["1:II.10","1:II.9"],"implied":[{"id":"1:II.3","via":"1:II.9"},{"id":"1:II.7","via":"1:II.9"}],"depth":5,"weight":0,"pos":[2629.2,889.1,6],"landmark":false,"img":{"s":[983,76],"p":[983,534]}},{"id":"1:II.14","label":"II.14","course":"1","kind":"Satz","chapter":"II","name":null,"page":20,"title":"k-elementige Teilmengen","note":null,"deps":["1:II.13","1:II.3","1:II.9"],"links":["1:II.13","1:II.9"],"implied":[{"id":"1:II.3","via":"1:II.9"}],"depth":5,"weight":0,"pos":[2673.1,891.2,6],"landmark":false,"img":{"s":[983,80],"p":[983,611]}},{"id":"1:IV.3","label":"IV.3","course":"1","kind":"Definition","chapter":"IV","name":null,"page":40,"title":"Abzählbar, überabzählbar","note":null,"deps":["1:IV.1","1:II.9"],"links":["1:IV.1","1:II.9"],"implied":[],"depth":5,"weight":2,"pos":[797.5,1872.9,8.1],"landmark":false,"img":{"s":[983,291]}},{"id":"L:5.12","label":"5.12","course":"L","kind":"Lemma","chapter":"5","name":"Multiplikation mit Inversen","page":43,"title":"Gleichungen in Gruppen eindeutig lösbar","note":null,"deps":["L:5.9"],"links":["L:5.9"],"implied":[],"depth":5,"weight":25,"pos":[5062.4,892.6,13.5],"landmark":false,"img":{"s":[983,68],"p":[983,417]}},{"id":"L:5.14","label":"5.14","course":"L","kind":"Definition","chapter":"5","name":null,"page":44,"title":"Permutation, symmetrische Gruppe","note":null,"deps":["L:5.9","L:4.15","L:4.17"],"links":["L:5.9","L:4.15","L:4.17"],"implied":[],"depth":5,"weight":104,"pos":[5195.2,850.5,21.3],"landmark":false,"img":{"s":[983,224]}},{"id":"L:5.22","label":"5.22","course":"L","kind":"Definition","chapter":"5","name":null,"page":48,"title":"Untergruppe","note":null,"deps":["L:5.9"],"links":["L:5.9"],"implied":[],"depth":5,"weight":159,"pos":[5316.8,881.6,24.9],"landmark":false,"img":{"s":[983,100]}},{"id":"L:5.28","label":"5.28","course":"L","kind":"Definition","chapter":"5","name":null,"page":49,"title":"Gruppenhomomorphismus","note":null,"deps":["L:5.9","L:4.13"],"links":["L:5.9"],"implied":[{"id":"L:4.13","via":"L:5.9"}],"depth":5,"weight":0,"pos":[5112.1,906.4,6],"landmark":false,"img":{"s":[983,465]}},{"id":"L:5.30","label":"5.30","course":"L","kind":"Definition","chapter":"5","name":null,"page":50,"title":"Ring","note":null,"deps":["L:5.9"],"links":["L:5.9"],"implied":[],"depth":5,"weight":531,"pos":[5114.3,840.2,28.2],"landmark":false,"img":{"s":[983,467]}},{"id":"L:5.72","label":"5.72","course":"L","kind":"Satz","chapter":"5","name":null,"page":67,"title":"Einheiten von ℤ/nℤ bilden eine Gruppe","note":null,"deps":["L:5.9","L:4.24"],"links":["L:5.9","L:4.24"],"implied":[],"depth":5,"weight":5,"pos":[5250.5,879.9,9.4],"landmark":false,"img":{"s":[983,140],"p":[983,340]}},{"id":"L:21.1","label":"21.1","course":"L","kind":"Definition","chapter":"21","name":null,"page":260,"title":"Gruppenaktion","note":null,"deps":["L:5.9","L:4.13"],"links":["L:5.9"],"implied":[{"id":"L:4.13","via":"L:5.9"}],"depth":5,"weight":19,"pos":[7019,1392.2,12.5],"landmark":false,"img":{"s":[983,697]}},{"id":"L:21.33","label":"21.33","course":"L","kind":"Satz","chapter":"21","name":null,"page":272,"title":"Euklidische Isometrien bilden eine Gruppe","note":null,"deps":["L:21.31","L:5.9"],"links":["L:21.31","L:5.9"],"implied":[],"depth":5,"weight":0,"pos":[7064.5,1414.1,6],"landmark":false,"img":{"s":[983,77]}},{"id":"1:I.6","label":"I.6","course":"1","kind":"Satz","chapter":"I","name":null,"page":6,"title":"Rechenregeln im Körper","note":null,"deps":["1:I.5","1:I.3","1:K1","1:K2","1:K3","1:K4","1:K5","1:K7","1:K9"],"links":["1:I.5"],"implied":[{"id":"1:I.3","via":"1:I.5"},{"id":"1:K1","via":"1:I.5"},{"id":"1:K2","via":"1:I.5"},{"id":"1:K3","via":"1:I.5"},{"id":"1:K4","via":"1:I.5"},{"id":"1:K5","via":"1:I.5"},{"id":"1:K7","via":"1:I.5"},{"id":"1:K9","via":"1:I.5"}],"depth":6,"weight":497,"pos":[1365.2,961.9,28.2],"landmark":false,"img":{"s":[983,316],"p":[983,772]}},{"id":"1:I.13","label":"I.13","course":"1","kind":"Satz","chapter":"I","name":null,"page":10,"title":"Äquivalente Formen der Vollständigkeit","note":null,"deps":["1:I.12","1:I.11"],"links":["1:I.12"],"implied":[{"id":"1:I.11","via":"1:I.12"}],"depth":6,"weight":1,"pos":[1394.3,900.7,7.5],"landmark":false,"img":{"s":[983,319],"p":[983,887]}},{"id":"1:I.16","label":"I.16","course":"1","kind":"Satz","chapter":"I","name":null,"page":13,"title":"ℝ ist eindeutig","note":"Beweis nicht im Skript (verweist auf Ebbinghaus/Landau)","deps":["1:I.12","1:I.7"],"links":["1:I.12"],"implied":[{"id":"1:I.7","via":"1:I.12"}],"depth":6,"weight":548,"pos":[1529.7,1010.8,28.2],"landmark":false,"img":{"s":[983,208]}},{"id":"1:I.18","label":"I.18","course":"1","kind":"Satz","chapter":"I","name":"Satz von Archimedes","page":13,"title":"Archimedes","note":null,"deps":["1:I.12","1:I.17","1:I.11"],"links":["1:I.12","1:I.17"],"implied":[{"id":"1:I.11","via":"1:I.12"}],"depth":6,"weight":51,"pos":[1297.8,999,16.7],"landmark":true,"img":{"s":[983,104],"p":[983,873]}},{"id":"1:IV.4","label":"IV.4","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":41,"title":"Surjektion von ℕ ⇒ abzählbar","note":null,"deps":["1:IV.3","1:II.2","1:II.3"],"links":["1:IV.3","1:II.2"],"implied":[{"id":"1:II.3","via":"1:IV.3"}],"depth":6,"weight":1,"pos":[849.7,1918.8,7.5],"landmark":false,"img":{"s":[983,73],"p":[983,395]}},{"id":"L:5.17","label":"5.17","course":"L","kind":"Satz","chapter":"5","name":"S m wird von Transpositionen erzeugt","page":45,"title":"Sₘ wird von Transpositionen erzeugt","note":null,"deps":["L:5.14","1:II.3"],"links":["L:5.14","1:II.3"],"implied":[],"depth":6,"weight":101,"pos":[5265.9,988.8,21.1],"landmark":false,"img":{"s":[983,68],"p":[983,825]}},{"id":"L:5.18","label":"5.18","course":"L","kind":"Definition","chapter":"5","name":null,"page":46,"title":"Fehlstandszahl, gerade/ungerade Permutationen","note":null,"deps":["L:5.14"],"links":["L:5.14"],"implied":[],"depth":6,"weight":96,"pos":[5368.2,957.3,20.7],"landmark":false,"img":{"s":[983,599]}},{"id":"L:5.25","label":"5.25","course":"L","kind":"Satz","chapter":"5","name":"Untergruppen-Kriterium","page":48,"title":"Untergruppenkriterium","note":null,"deps":["L:5.22","L:5.12"],"links":["L:5.22","L:5.12"],"implied":[],"depth":6,"weight":22,"pos":[5129.3,955.9,13],"landmark":false,"img":{"s":[983,182],"p":[983,169]}},{"id":"L:5.26","label":"5.26","course":"L","kind":"Definition","chapter":"5","name":null,"page":49,"title":"Erzeugte und zyklische Untergruppe","note":null,"deps":["L:5.22"],"links":["L:5.22"],"implied":[],"depth":6,"weight":0,"pos":[5154,893.2,6],"landmark":false,"img":{"s":[983,195]}},{"id":"L:5.34","label":"5.34","course":"L","kind":"Definition","chapter":"5","name":null,"page":52,"title":"Nullteiler","note":null,"deps":["L:5.30"],"links":["L:5.30"],"implied":[],"depth":6,"weight":0,"pos":[5310,949.5,6],"landmark":false,"img":{"s":[983,136]}},{"id":"L:5.36","label":"5.36","course":"L","kind":"Definition","chapter":"5","name":null,"page":52,"title":"Ringhomomorphismus","note":null,"deps":["L:5.30"],"links":["L:5.30"],"implied":[],"depth":6,"weight":0,"pos":[5080.5,940.8,6],"landmark":false,"img":{"s":[983,194]}},{"id":"L:5.38","label":"5.38","course":"L","kind":"Definition","chapter":"5","name":null,"page":52,"title":"Körper","note":null,"deps":["L:5.30"],"links":["L:5.30"],"implied":[],"depth":6,"weight":528,"pos":[5200.8,940.1,28.2],"landmark":true,"img":{"s":[983,408]}},{"id":"L:5.73","label":"5.73","course":"L","kind":"Definition","chapter":"5","name":" /n ∗ , ·","page":68,"title":"Einheitengruppe","note":null,"deps":["L:5.72"],"links":["L:5.72"],"implied":[],"depth":6,"weight":4,"pos":[5268.8,926.8,9],"landmark":false,"img":{"s":[983,81]}},{"id":"1:I.8","label":"I.8","course":"1","kind":"Satz","chapter":"I","name":null,"page":7,"title":"Rechenregeln für Ungleichungen","note":null,"deps":["1:I.7","1:O1","1:O2","1:I.6"],"links":["1:I.7","1:I.6"],"implied":[{"id":"1:O1","via":"1:I.7"},{"id":"1:O2","via":"1:I.7"}],"depth":7,"weight":494,"pos":[1429.3,1050.6,28.2],"landmark":false,"img":{"s":[983,618],"p":[983,897]}},{"id":"1:II.5","label":"II.5","course":"1","kind":"Satz","chapter":"II","name":"Geometrische Summe","page":17,"title":"Geometrische Summe","note":null,"deps":["1:II.3","1:I.6"],"links":["1:II.3","1:I.6"],"implied":[],"depth":7,"weight":88,"pos":[2470.4,1098.9,20.1],"landmark":false,"img":{"s":[983,142],"p":[983,393]}},{"id":"1:III.1","label":"III.1","course":"1","kind":"Definition","chapter":"III","name":null,"page":22,"title":"Folge","note":null,"deps":["1:II.7","1:I.16"],"links":["1:II.7","1:I.16"],"implied":[],"depth":7,"weight":502,"pos":[1922.6,1497.3,28.2],"landmark":false,"img":{"s":[983,469]}},{"id":"L:3.1","label":"3.1","course":"L","kind":"Definition","chapter":"3","name":null,"page":14,"title":"Lineares Gleichungssystem","note":null,"deps":["1:VOR","1:I.16"],"links":["1:I.16"],"implied":[{"id":"1:VOR","via":"1:I.16"}],"depth":7,"weight":91,"pos":[5131.7,345.3,20.3],"landmark":false,"img":{"s":[983,443]}},{"id":"2:I.1","label":"I.1","course":"2","kind":"Definition","chapter":"I","name":null,"page":3,"title":"Metrischer Raum","note":null,"deps":["1:VOR","1:I.16"],"links":["1:I.16"],"implied":[{"id":"1:VOR","via":"1:I.16"}],"depth":7,"weight":174,"pos":[2479.3,4864.9,25.8],"landmark":false,"img":{"s":[983,561]}},{"id":"1:I.19","label":"I.19","course":"1","kind":"Satz","chapter":"I","name":null,"page":14,"title":"1/n < ε","note":null,"deps":["1:I.18"],"links":["1:I.18"],"implied":[],"depth":7,"weight":50,"pos":[1353.5,1037.9,16.6],"landmark":false,"img":{"s":[983,124],"p":[983,295]}},{"id":"1:IV.5","label":"IV.5","course":"1","kind":"Satz","chapter":"IV","name":null,"page":41,"title":"ℤ und ℚ sind abzählbar","note":null,"deps":["1:IV.4"],"links":["1:IV.4"],"implied":[],"depth":7,"weight":0,"pos":[739.2,2008.2,6],"landmark":false,"img":{"s":[983,39],"p":[983,1149]}},{"id":"L:5.19","label":"5.19","course":"L","kind":"Lemma","chapter":"5","name":"Anzahl Transpositionen","page":46,"title":"Parität der Anzahl der Transpositionen","note":null,"deps":["L:5.17","L:5.18"],"links":["L:5.17","L:5.18"],"implied":[],"depth":7,"weight":94,"pos":[5152,1017.4,20.5],"landmark":false,"img":{"s":[983,101],"p":[983,1394]}},{"id":"L:12.1","label":"12.1","course":"L","kind":"Definition","chapter":"12","name":null,"page":138,"title":"Signum einer Permutation","note":null,"deps":["L:5.18"],"links":["L:5.18"],"implied":[],"depth":7,"weight":93,"pos":[6303.1,1702.1,20.5],"landmark":false,"img":{"s":[983,158]}},{"id":"L:5.41","label":"5.41","course":"L","kind":"Definition","chapter":"5","name":null,"page":53,"title":"Körperhomomorphismus","note":null,"deps":["L:5.38"],"links":["L:5.38"],"implied":[],"depth":7,"weight":0,"pos":[5076,1034.2,6],"landmark":false,"img":{"s":[983,207]}},{"id":"L:5.43","label":"5.43","course":"L","kind":"Definition","chapter":"5","name":null,"page":53,"title":"Charakteristik eines Körpers","note":null,"deps":["L:5.38"],"links":["L:5.38"],"implied":[],"depth":7,"weight":0,"pos":[5097.5,995.9,6],"landmark":false,"img":{"s":[983,282]}},{"id":"L:5.49","label":"5.49","course":"L","kind":"Definition","chapter":"5","name":null,"page":56,"title":"Matrix über einem Körper","note":null,"deps":["L:5.38"],"links":["L:5.38"],"implied":[],"depth":7,"weight":183,"pos":[5238.2,1063.2,26.3],"landmark":false,"img":{"s":[983,1662]}},{"id":"L:5.60","label":"5.60","course":"L","kind":"Definition","chapter":"5","name":null,"page":62,"title":"Polynom über einem Körper","note":null,"deps":["L:5.38"],"links":["L:5.38"],"implied":[],"depth":7,"weight":56,"pos":[5313.5,1057,17.2],"landmark":false,"img":{"s":[983,1238]}},{"id":"L:6.1","label":"6.1","course":"L","kind":"Definition","chapter":"6","name":null,"page":73,"title":"Vektorraum","note":null,"deps":["L:5.9","L:5.38"],"links":["L:5.38"],"implied":[{"id":"L:5.9","via":"L:5.38"}],"depth":7,"weight":512,"pos":[6445.5,1312,28.2],"landmark":true,"img":{"s":[983,1041]}},{"id":"L:5.74","label":"5.74","course":"L","kind":"Satz","chapter":"5","name":null,"page":68,"title":"Einheiten = zu n teilerfremde Restklassen","note":null,"deps":["L:5.73","L:5.69"],"links":["L:5.73","L:5.69"],"implied":[],"depth":7,"weight":0,"pos":[5209.3,1005.8,6],"landmark":false,"img":{"s":[983,104],"p":[983,418]}},{"id":"L:5.77","label":"5.77","course":"L","kind":"Definition","chapter":"5","name":null,"page":68,"title":"Eulersche φ-Funktion","note":null,"deps":["L:5.73"],"links":["L:5.73"],"implied":[],"depth":7,"weight":2,"pos":[5325.9,1001,8.1],"landmark":false,"img":{"s":[983,154]}},{"id":"1:I.10","label":"I.10","course":"1","kind":"Satz","chapter":"I","name":null,"page":8,"title":"Eigenschaften des Betrags, Dreiecksungleichung","note":null,"deps":["1:I.9","1:I.8","1:I.6"],"links":["1:I.9","1:I.8"],"implied":[{"id":"1:I.6","via":"1:I.8"}],"depth":8,"weight":482,"pos":[1471.1,1128.6,28.2],"landmark":false,"img":{"s":[983,358],"p":[983,1003]}},{"id":"1:I.15","label":"I.15","course":"1","kind":"Satz","chapter":"I","name":null,"page":12,"title":"ℚ ist nicht vollständig","note":null,"deps":["1:I.13","1:I.14","1:I.8"],"links":["1:I.13","1:I.14","1:I.8"],"implied":[],"depth":8,"weight":0,"pos":[1493.6,1066.4,6],"landmark":false,"img":{"s":[983,38],"p":[983,944]}},{"id":"1:II.6","label":"II.6","course":"1","kind":"Satz","chapter":"II","name":"Bernoullische Ungleichung","page":17,"title":"Bernoullische Ungleichung","note":null,"deps":["1:II.3","1:I.8"],"links":["1:II.3","1:I.8"],"implied":[],"depth":8,"weight":13,"pos":[2576.9,1071.8,11.4],"landmark":false,"img":{"s":[983,104],"p":[983,296]}},{"id":"1:VII.5","label":"VII.5","course":"1","kind":"Definition","chapter":"VII","name":null,"page":82,"title":"Monotone Funktionen","note":null,"deps":["1:I.8"],"links":["1:I.8"],"implied":[],"depth":8,"weight":24,"pos":[1247.9,2820.1,13.3],"landmark":false,"img":{"s":[983,148]}},{"id":"1:VIII.11","label":"VIII.11","course":"1","kind":"Definition","chapter":"VIII","name":null,"page":99,"title":"Lokales Minimum / Maximum","note":null,"deps":["1:I.8"],"links":["1:I.8"],"implied":[],"depth":8,"weight":132,"pos":[2200.6,2636.7,23.2],"landmark":false,"img":{"s":[983,247]}},{"id":"1:VIII.21","label":"VIII.21","course":"1","kind":"Definition","chapter":"VIII","name":null,"page":104,"title":"Konvexe Funktionen","note":null,"deps":["1:I.8"],"links":["1:I.8"],"implied":[],"depth":8,"weight":3,"pos":[2263.4,2625.1,8.6],"landmark":false,"img":{"s":[983,580]}},{"id":"1:X.1","label":"X.1","course":"1","kind":"Definition","chapter":"X","name":"Zerlegung","page":118,"title":"Zerlegung","note":null,"deps":["1:I.8"],"links":["1:I.8"],"implied":[],"depth":8,"weight":124,"pos":[3237.9,2154,22.7],"landmark":false,"img":{"s":[983,198]}},{"id":"1:III.2","label":"III.2","course":"1","kind":"Definition","chapter":"III","name":null,"page":22,"title":"Konvergenz, Grenzwert","note":null,"deps":["1:III.1","1:I.9"],"links":["1:III.1","1:I.9"],"implied":[],"depth":8,"weight":497,"pos":[1927.5,1589.4,28.2],"landmark":false,"img":{"s":[983,1345]}},{"id":"1:III.5","label":"III.5","course":"1","kind":"Definition","chapter":"III","name":null,"page":24,"title":"Beschränkte Folgen","note":null,"deps":["1:III.1","1:I.9"],"links":["1:III.1","1:I.9"],"implied":[],"depth":8,"weight":483,"pos":[2078.5,1581.2,28.2],"landmark":false,"img":{"s":[983,488]}},{"id":"1:III.9","label":"III.9","course":"1","kind":"Definition","chapter":"III","name":null,"page":27,"title":"Monotone Folgen","note":null,"deps":["1:III.1"],"links":["1:III.1"],"implied":[],"depth":8,"weight":481,"pos":[1849.6,1547.3,28.2],"landmark":false,"img":{"s":[983,127]}},{"id":"1:III.16","label":"III.16","course":"1","kind":"Definition","chapter":"III","name":null,"page":34,"title":"Teilfolge","note":null,"deps":["1:III.1"],"links":["1:III.1"],"implied":[],"depth":8,"weight":241,"pos":[1774.3,1593.8,28.2],"landmark":false,"img":{"s":[983,258]}},{"id":"1:III.22","label":"III.22","course":"1","kind":"Definition","chapter":"III","name":null,"page":37,"title":"Cauchy-Folge","note":null,"deps":["1:III.1","1:I.9"],"links":["1:III.1","1:I.9"],"implied":[],"depth":8,"weight":278,"pos":[2000.5,1539.3,28.2],"landmark":false,"img":{"s":[983,164]}},{"id":"L:3.2","label":"3.2","course":"L","kind":"Definition","chapter":"3","name":null,"page":15,"title":"Lösungsmenge eines LGS","note":null,"deps":["L:3.1"],"links":["L:3.1"],"implied":[],"depth":8,"weight":83,"pos":[5112.9,414.7,19.7],"landmark":false,"img":{"s":[983,221]}},{"id":"L:3.3","label":"3.3","course":"L","kind":"Definition","chapter":"3","name":null,"page":15,"title":"Elementaroperationen","note":null,"deps":["L:3.1"],"links":["L:3.1"],"implied":[],"depth":8,"weight":83,"pos":[5181.9,396.9,19.7],"landmark":false,"img":{"s":[983,322]}},{"id":"L:3.6","label":"3.6","course":"L","kind":"Definition","chapter":"3","name":null,"page":18,"title":"Matrix (Einführung)","note":null,"deps":["L:3.1"],"links":["L:3.1"],"implied":[],"depth":8,"weight":82,"pos":[5253,402,19.6],"landmark":false,"img":{"s":[983,825]}},{"id":"2:I.3","label":"I.3","course":"2","kind":"Definition","chapter":"I","name":null,"page":4,"title":"Offene Kugel","note":null,"deps":["2:I.1"],"links":["2:I.1"],"implied":[],"depth":8,"weight":173,"pos":[2543.7,4918,25.7],"landmark":false,"img":{"s":[983,218]}},{"id":"1:I.20","label":"I.20","course":"1","kind":"Satz","chapter":"I","name":"Q ist dicht in R","page":14,"title":"ℚ ist dicht in ℝ","note":null,"deps":["1:I.19","1:I.18"],"links":["1:I.19"],"implied":[{"id":"1:I.18","via":"1:I.19"}],"depth":8,"weight":49,"pos":[1385.6,1113.8,16.5],"landmark":false,"img":{"s":[983,77],"p":[983,429]}},{"id":"L:5.20","label":"5.20","course":"L","kind":"Korollar","chapter":"5","name":null,"page":48,"title":"Alternierende Gruppe","note":null,"deps":["L:5.19","L:5.25"],"links":["L:5.19","L:5.25"],"implied":[],"depth":8,"weight":0,"pos":[5111.7,1060,6],"landmark":false,"img":{"s":[983,70]}},{"id":"L:12.2","label":"12.2","course":"L","kind":"Satz","chapter":"12","name":null,"page":138,"title":"Signum über die Anzahl der Transpositionen","note":null,"deps":["L:12.1","L:5.19"],"links":["L:12.1","L:5.19"],"implied":[],"depth":8,"weight":92,"pos":[6189.3,1778.6,20.4],"landmark":false,"img":{"s":[983,68],"p":[983,77]}},{"id":"L:5.50","label":"5.50","course":"L","kind":"Definition","chapter":"5","name":null,"page":57,"title":"Matrizenprodukt","note":null,"deps":["L:5.49"],"links":["L:5.49"],"implied":[],"depth":8,"weight":114,"pos":[5162.9,1091.2,22],"landmark":false,"img":{"s":[983,528]}},{"id":"L:5.61","label":"5.61","course":"L","kind":"Satz","chapter":"5","name":" [X], +, ·","page":63,"title":"K[X] ist ein kommutativer Ring","note":null,"deps":["L:5.60","L:5.30"],"links":["L:5.60"],"implied":[{"id":"L:5.30","via":"L:5.60"}],"depth":8,"weight":0,"pos":[5104.2,1103.3,6],"landmark":false,"img":{"s":[983,36],"p":[983,596]}},{"id":"L:13.5","label":"13.5","course":"L","kind":"Definition","chapter":"13","name":null,"page":153,"title":"Nullstelle eines Polynoms","note":null,"deps":["L:5.60"],"links":["L:5.60"],"implied":[],"depth":8,"weight":53,"pos":[6234.6,1654.4,16.9],"landmark":false,"img":{"s":[983,176]}},{"id":"L:6.2","label":"6.2","course":"L","kind":"Satz","chapter":"6","name":null,"page":74,"title":"Rechenregeln im Vektorraum","note":null,"deps":["L:6.1"],"links":["L:6.1"],"implied":[],"depth":8,"weight":100,"pos":[6515.6,1353,21],"landmark":false,"img":{"s":[983,141],"p":[983,2833]}},{"id":"L:6.4","label":"6.4","course":"L","kind":"Definition","chapter":"6","name":null,"page":77,"title":"Linearkombination","note":null,"deps":["L:6.1"],"links":["L:6.1"],"implied":[],"depth":8,"weight":241,"pos":[6596.9,1352.5,28.2],"landmark":false,"img":{"s":[983,286]}},{"id":"L:8.1","label":"8.1","course":"L","kind":"Definition","chapter":"8","name":null,"page":94,"title":"Untervektorraum","note":null,"deps":["L:6.1","L:5.22"],"links":["L:6.1","L:5.22"],"implied":[],"depth":8,"weight":146,"pos":[4760.7,1612.2,24.1],"landmark":false,"img":{"s":[983,497]}},{"id":"L:9.1","label":"9.1","course":"L","kind":"Definition","chapter":"9","name":null,"page":108,"title":"Lineare Abbildung","note":null,"deps":["L:6.1","L:4.13"],"links":["L:6.1"],"implied":[{"id":"L:4.13","via":"L:6.1"}],"depth":8,"weight":225,"pos":[5611.1,1569,28.2],"landmark":false,"img":{"s":[983,184]}},{"id":"L:12.5","label":"12.5","course":"L","kind":"Definition","chapter":"12","name":null,"page":139,"title":"Determinantenfunktion","note":null,"deps":["L:6.1","L:5.38"],"links":["L:6.1"],"implied":[{"id":"L:5.38","via":"L:6.1"}],"depth":8,"weight":92,"pos":[6311.4,1774.5,20.4],"landmark":false,"img":{"s":[983,329]}},{"id":"L:18.1","label":"18.1","course":"L","kind":"Definition","chapter":"18","name":null,"page":187,"title":"Bilinearform, Skalarprodukt (reell)","note":null,"deps":["L:6.1","1:I.16"],"links":["L:6.1","1:I.16"],"implied":[],"depth":8,"weight":347,"pos":[7039.9,1621.1,28.2],"landmark":false,"img":{"s":[983,642]}},{"id":"L:21.4","label":"21.4","course":"L","kind":"Definition","chapter":"21","name":null,"page":262,"title":"Affiner Raum","note":null,"deps":["L:21.1","L:6.1"],"links":["L:21.1","L:6.1"],"implied":[],"depth":8,"weight":18,"pos":[7113.2,1552.1,12.4],"landmark":false,"img":{"s":[983,418]}},{"id":"2:III.6","label":"III.6","course":"2","kind":"Definition","chapter":"III","name":null,"page":31,"title":"Konvexe Menge","note":null,"deps":["L:6.1"],"links":["L:6.1"],"implied":[],"depth":8,"weight":56,"pos":[4171.8,5018.8,17.2],"landmark":false,"img":{"s":[983,99]}},{"id":"L:5.79","label":"5.79","course":"L","kind":"Satz","chapter":"5","name":"Euler-Fermat","page":68,"title":"Satz von Euler-Fermat","note":null,"deps":["L:5.77","L:5.12"],"links":["L:5.77","L:5.12"],"implied":[],"depth":8,"weight":1,"pos":[5214.6,1124.6,7.5],"landmark":false,"img":{"s":[983,119],"p":[983,277]}},{"id":"L:18.14","label":"18.14","course":"L","kind":"Definition","chapter":"18","name":null,"page":194,"title":"Norm","note":null,"deps":["L:6.1","1:I.10"],"links":["L:6.1","1:I.10"],"implied":[],"depth":9,"weight":25,"pos":[6978.4,1661.7,13.5],"landmark":false,"img":{"s":[983,359]}},{"id":"1:X.2","label":"X.2","course":"1","kind":"Definition","chapter":"X","name":"Riemannsche Summe","page":118,"title":"Riemannsche Summe","note":null,"deps":["1:X.1"],"links":["1:X.1"],"implied":[],"depth":9,"weight":123,"pos":[3316.1,2240.5,22.6],"landmark":false,"img":{"s":[983,455]}},{"id":"1:III.4","label":"III.4","course":"1","kind":"Satz","chapter":"III","name":null,"page":23,"title":"Eindeutigkeit des Grenzwerts","note":null,"deps":["1:III.2","1:III.3","1:I.10"],"links":["1:III.2","1:III.3","1:I.10"],"implied":[],"depth":9,"weight":158,"pos":[2005.1,1624.3,24.9],"landmark":false,"img":{"s":[983,73],"p":[983,641]}},{"id":"1:III.8","label":"III.8","course":"1","kind":"Satz","chapter":"III","name":null,"page":27,"title":"Grenzwerte und Ungleichungen, Sandwich","note":null,"deps":["1:III.2","1:I.8"],"links":["1:III.2","1:I.8"],"implied":[],"depth":9,"weight":476,"pos":[1780.2,1687.3,28.2],"landmark":false,"img":{"s":[983,337],"p":[983,634]}},{"id":"1:III.13","label":"III.13","course":"1","kind":"Definition","chapter":"III","name":"Intervallschachtelung","page":31,"title":"Intervallschachtelung","note":null,"deps":["1:III.2"],"links":["1:III.2"],"implied":[],"depth":9,"weight":474,"pos":[1852.2,1635.8,28.2],"landmark":false,"img":{"s":[983,209]}},{"id":"3:I.4","label":"I.4","course":"3","kind":"Definition","chapter":"I","name":null,"page":4,"title":"Konvergenz in ℝ̄","note":null,"deps":["1:III.2"],"links":["1:III.2"],"implied":[],"depth":9,"weight":68,"pos":[3100.3,7261,18.4],"landmark":false,"img":{"s":[983,825]}},{"id":"1:III.6","label":"III.6","course":"1","kind":"Satz","chapter":"III","name":null,"page":24,"title":"Konvergent ⇒ beschränkt","note":null,"deps":["1:III.2","1:III.5","1:I.10"],"links":["1:III.2","1:III.5","1:I.10"],"implied":[],"depth":9,"weight":475,"pos":[1996.9,1709,28.2],"landmark":false,"img":{"s":[983,37],"p":[983,621]}},{"id":"1:III.10","label":"III.10","course":"1","kind":"Satz","chapter":"III","name":"Konvergenzkriterium der Monotonie und Beschränktheit","page":27,"title":"Monotonie-Kriterium","note":null,"deps":["1:I.12","1:I.17","1:III.9","1:III.5","1:III.2"],"links":["1:I.17","1:III.9","1:III.5","1:III.2"],"implied":[{"id":"1:I.12","via":"1:III.9"}],"depth":9,"weight":480,"pos":[2076.6,1670.5,28.2],"landmark":true,"img":{"s":[983,110],"p":[983,2484]}},{"id":"1:III.17","label":"III.17","course":"1","kind":"Definition","chapter":"III","name":"Häufungspunkt","page":34,"title":"Häufungspunkt einer Folge","note":null,"deps":["1:III.16","1:III.2"],"links":["1:III.16","1:III.2"],"implied":[],"depth":9,"weight":229,"pos":[1860.9,1723.9,28.2],"landmark":false,"img":{"s":[983,214]}},{"id":"1:III.23","label":"III.23","course":"1","kind":"Satz","chapter":"III","name":null,"page":37,"title":"Konvergent ⇒ Cauchy","note":null,"deps":["1:III.22","1:III.2","1:I.10"],"links":["1:III.22","1:III.2","1:I.10"],"implied":[],"depth":9,"weight":98,"pos":[1924.2,1673.2,20.8],"landmark":false,"img":{"s":[983,37],"p":[983,359]}},{"id":"L:3.4","label":"3.4","course":"L","kind":"Satz","chapter":"3","name":null,"page":15,"title":"Elementaroperationen ändern die Lösungsmenge nicht","note":null,"deps":["L:3.2","L:3.3"],"links":["L:3.2","L:3.3"],"implied":[],"depth":9,"weight":82,"pos":[5179,468.1,19.6],"landmark":false,"img":{"s":[983,130],"p":[983,1719]}},{"id":"2:I.4","label":"I.4","course":"2","kind":"Definition","chapter":"I","name":null,"page":4,"title":"Offene Menge","note":null,"deps":["2:I.3"],"links":["2:I.3"],"implied":[],"depth":9,"weight":133,"pos":[2658.4,4993.8,23.3],"landmark":false,"img":{"s":[983,268]}},{"id":"2:I.6","label":"I.6","course":"2","kind":"Lemma","chapter":"I","name":"Hausdorff-Trennungseigenschaft","page":4,"title":"Hausdorff-Eigenschaft","note":null,"deps":["2:I.3","2:I.1"],"links":["2:I.3"],"implied":[{"id":"2:I.1","via":"2:I.3"}],"depth":9,"weight":110,"pos":[2542.3,4997.4,21.7],"landmark":false,"img":{"s":[983,169],"p":[983,76]}},{"id":"2:I.11","label":"I.11","course":"2","kind":"Definition","chapter":"I","name":null,"page":6,"title":"Inneres, Abschluss, Rand","note":null,"deps":["2:I.3"],"links":["2:I.3"],"implied":[],"depth":9,"weight":19,"pos":[2598.4,4962.1,12.5],"landmark":false,"img":{"s":[983,681]}},{"id":"2:I.13","label":"I.13","course":"2","kind":"Definition","chapter":"I","name":null,"page":7,"title":"Häufungspunkt, isolierter Punkt","note":null,"deps":["2:I.3"],"links":["2:I.3"],"implied":[],"depth":9,"weight":0,"pos":[2600.1,5012.6,6],"landmark":false,"img":{"s":[983,397]}},{"id":"2:I.17","label":"I.17","course":"2","kind":"Definition","chapter":"I","name":null,"page":8,"title":"Stetigkeit zwischen metrischen Räumen","note":null,"deps":["2:I.1","2:I.3"],"links":["2:I.3"],"implied":[{"id":"2:I.1","via":"2:I.3"}],"depth":9,"weight":123,"pos":[2475.5,4960.5,22.6],"landmark":false,"img":{"s":[983,245]}},{"id":"2:III.9","label":"III.9","course":"2","kind":"Definition","chapter":"III","name":null,"page":33,"title":"Lokales Minimum / Maximum","note":null,"deps":["2:I.3"],"links":["2:I.3"],"implied":[],"depth":9,"weight":5,"pos":[4138.2,5112.3,9.4],"landmark":false,"img":{"s":[983,229]}},{"id":"L:12.3","label":"12.3","course":"L","kind":"Satz","chapter":"12","name":null,"page":138,"title":"Signum ist multiplikativ","note":null,"deps":["L:5.17","L:12.2"],"links":["L:12.2"],"implied":[{"id":"L:5.17","via":"L:12.2"}],"depth":9,"weight":91,"pos":[6320.7,1846.6,20.3],"landmark":false,"img":{"s":[983,104],"p":[983,266]}},{"id":"L:5.52","label":"5.52","course":"L","kind":"Satz","chapter":"5","name":null,"page":58,"title":"Die n×n-Matrizen bilden einen Ring","note":null,"deps":["L:5.50","L:5.30"],"links":["L:5.50"],"implied":[{"id":"L:5.30","via":"L:5.50"}],"depth":9,"weight":107,"pos":[5127.7,1158,21.5],"landmark":false,"img":{"s":[983,133],"p":[983,454]}},{"id":"L:5.59","label":"5.59","course":"L","kind":"Satz","chapter":"5","name":null,"page":62,"title":"Rechenregeln für die Transponierte","note":null,"deps":["L:5.50"],"links":["L:5.50"],"implied":[],"depth":9,"weight":44,"pos":[5282.6,1170.3,15.9],"landmark":false,"img":{"s":[983,274],"p":[983,341]}},{"id":"L:6.7","label":"6.7","course":"L","kind":"Definition","chapter":"6","name":null,"page":78,"title":"Lineare Unabhängigkeit","note":null,"deps":["L:6.4"],"links":["L:6.4"],"implied":[],"depth":9,"weight":229,"pos":[6461.6,1413.7,28.2],"landmark":false,"img":{"s":[983,636]}},{"id":"L:6.13","label":"6.13","course":"L","kind":"Definition","chapter":"6","name":null,"page":82,"title":"Lineare Hülle (Spann)","note":null,"deps":["L:6.4"],"links":["L:6.4"],"implied":[],"depth":9,"weight":230,"pos":[6549.1,1427,28.2],"landmark":false,"img":{"s":[983,134]}},{"id":"L:8.2","label":"8.2","course":"L","kind":"Lemma","chapter":"8","name":"UVR-Kriterium","page":94,"title":"Untervektorraum-Kriterium","note":null,"deps":["L:8.1"],"links":["L:8.1"],"implied":[],"depth":9,"weight":132,"pos":[4698.5,1674.9,23.2],"landmark":false,"img":{"s":[983,220],"p":[983,356]}},{"id":"L:8.26","label":"8.26","course":"L","kind":"Lemma","chapter":"8","name":null,"page":105,"title":"Kongruenz modulo eines Untervektorraums","note":null,"deps":["L:8.1","L:4.22"],"links":["L:8.1","L:4.22"],"implied":[],"depth":9,"weight":14,"pos":[4765.2,1679.8,11.6],"landmark":false,"img":{"s":[983,149],"p":[983,295]}},{"id":"L:9.2","label":"9.2","course":"L","kind":"Lemma","chapter":"9","name":null,"page":108,"title":"Lineare Abbildungen erhalten die Null","note":null,"deps":["L:9.1","L:6.2"],"links":["L:9.1","L:6.2"],"implied":[],"depth":9,"weight":99,"pos":[5536.8,1601.8,20.9],"landmark":false,"img":{"s":[983,71],"p":[983,176]}},{"id":"L:9.3","label":"9.3","course":"L","kind":"Lemma","chapter":"9","name":"linear","page":108,"title":"Linear ⇔ verträglich mit Linearkombinationen","note":null,"deps":["L:9.1"],"links":["L:9.1"],"implied":[],"depth":9,"weight":2,"pos":[5452.7,1581.1,8.1],"landmark":false,"img":{"s":[983,130],"p":[983,103]}},{"id":"L:9.4","label":"9.4","course":"L","kind":"Definition","chapter":"9","name":null,"page":108,"title":"Homomorphismus, Isomorphismus","note":null,"deps":["L:9.1","L:4.15"],"links":["L:9.1","L:4.15"],"implied":[],"depth":9,"weight":0,"pos":[5494.2,1561.1,6],"landmark":false,"img":{"s":[983,3069]}},{"id":"L:9.9","label":"9.9","course":"L","kind":"Definition","chapter":"9","name":null,"page":112,"title":"Kern","note":null,"deps":["L:9.1"],"links":["L:9.1"],"implied":[],"depth":9,"weight":108,"pos":[5472.6,1639.5,21.6],"landmark":false,"img":{"s":[983,134]}},{"id":"L:9.26","label":"9.26","course":"L","kind":"Definition","chapter":"9","name":null,"page":119,"title":"Summe und Vielfache linearer Abbildungen","note":null,"deps":["L:9.1"],"links":["L:9.1"],"implied":[],"depth":9,"weight":161,"pos":[5397.6,1615.9,25],"landmark":false,"img":{"s":[983,407]}},{"id":"L:17.1","label":"17.1","course":"L","kind":"Definition","chapter":"17","name":null,"page":167,"title":"Nilpotent","note":null,"deps":["L:9.1"],"links":["L:9.1"],"implied":[],"depth":9,"weight":8,"pos":[6263,2323.2,10.2],"landmark":false,"img":{"s":[983,433]}},{"id":"L:20.1","label":"20.1","course":"L","kind":"Definition","chapter":"20","name":null,"page":243,"title":"Bilinearform","note":null,"deps":["L:6.1","L:9.1"],"links":["L:9.1"],"implied":[{"id":"L:6.1","via":"L:9.1"}],"depth":9,"weight":40,"pos":[6834.4,2390.3,15.5],"landmark":false,"img":{"s":[983,494]}},{"id":"L:12.7","label":"12.7","course":"L","kind":"Korollar","chapter":"12","name":null,"page":139,"title":"Multilinearität und Alternierung","note":null,"deps":["L:12.5","L:5.17"],"links":["L:12.5","L:5.17"],"implied":[],"depth":9,"weight":91,"pos":[6202.2,1861,20.3],"landmark":false,"img":{"s":[983,605],"p":[983,360]}},{"id":"L:21.7","label":"21.7","course":"L","kind":"Definition","chapter":"21","name":null,"page":263,"title":"Affiner Unterraum","note":null,"deps":["L:21.4","L:8.1"],"links":["L:21.4","L:8.1"],"implied":[],"depth":9,"weight":6,"pos":[7101.3,1654.6,9.7],"landmark":false,"img":{"s":[983,588]}},{"id":"L:21.14","label":"21.14","course":"L","kind":"Definition","chapter":"21","name":null,"page":266,"title":"Affin unabhängig","note":null,"deps":["L:21.4"],"links":["L:21.4"],"implied":[],"depth":9,"weight":3,"pos":[7106.8,1604.6,8.6],"landmark":false,"img":{"s":[983,193]}},{"id":"L:21.18","label":"21.18","course":"L","kind":"Definition","chapter":"21","name":null,"page":267,"title":"Affine Abbildung","note":null,"deps":["L:21.4"],"links":["L:21.4"],"implied":[],"depth":9,"weight":7,"pos":[7223.2,1622.2,10],"landmark":false,"img":{"s":[983,150]}},{"id":"2:III.19","label":"III.19","course":"2","kind":"Definition","chapter":"III","name":null,"page":39,"title":"Konvexe Funktion im ℝⁿ","note":null,"deps":["2:III.6"],"links":["2:III.6"],"implied":[],"depth":9,"weight":2,"pos":[4173.4,5077.6,8.1],"landmark":false,"img":{"s":[983,378]}},{"id":"L:5.81","label":"5.81","course":"L","kind":"Satz","chapter":"5","name":null,"page":69,"title":"Grundlage des RSA-Verfahrens","note":null,"deps":["L:5.79"],"links":["L:5.79"],"implied":[],"depth":9,"weight":0,"pos":[5187.1,1160.9,6],"landmark":false,"img":{"s":[983,89],"p":[983,1068]}},{"id":"L:18.21","label":"18.21","course":"L","kind":"Lemma","chapter":"18","name":null,"page":198,"title":"Normierte Räume sind metrische Räume","note":null,"deps":["L:18.14","L:18.19"],"links":["L:18.14","L:18.19"],"implied":[],"depth":10,"weight":0,"pos":[7137.5,1685.7,6],"landmark":false,"img":{"s":[983,34],"p":[983,302]}},{"id":"2:I.2","label":"I.2","course":"2","kind":"Definition","chapter":"I","name":null,"page":3,"title":"Norm, normierter Raum","note":null,"deps":["1:I.16","L:18.14","L:6.1"],"links":["1:I.16","L:18.14"],"implied":[{"id":"L:6.1","via":"L:18.14"}],"depth":10,"weight":3,"pos":[2544.3,4851.7,8.6],"landmark":false,"img":{"s":[983,640]}},{"id":"3:I.13","label":"I.13","course":"3","kind":"Definition","chapter":"I","name":null,"page":10,"title":"Numerische Funktion","note":null,"deps":["3:I.4","3:I.1"],"links":["3:I.4","3:I.1"],"implied":[],"depth":10,"weight":67,"pos":[3152.9,7384.2,18.3],"landmark":false,"img":{"s":[983,127]}},{"id":"1:III.7","label":"III.7","course":"1","kind":"Satz","chapter":"III","name":null,"page":25,"title":"Grenzwertsätze (Summe, Produkt, Quotient)","note":null,"deps":["1:III.2","1:III.6","1:I.10"],"links":["1:III.6"],"implied":[{"id":"1:III.2","via":"1:III.6"},{"id":"1:I.10","via":"1:III.6"}],"depth":10,"weight":474,"pos":[2059.3,1771.8,28.2],"landmark":false,"img":{"s":[983,316],"p":[983,2703]}},{"id":"1:III.11","label":"III.11","course":"1","kind":"Definition","chapter":"III","name":"Eulersche Zahl","page":29,"title":"Eulersche Zahl e","note":null,"deps":["1:III.10","1:II.15","1:II.6","1:II.5"],"links":["1:III.10","1:II.15","1:II.6","1:II.5"],"implied":[],"depth":10,"weight":12,"pos":[1931.1,1736.9,11.2],"landmark":false,"img":{"s":[983,881]}},{"id":"1:III.18","label":"III.18","course":"1","kind":"Lemma","chapter":"III","name":null,"page":34,"title":"Häufungspunkt über ε-Umgebungen","note":null,"deps":["1:III.17","1:III.3","1:II.9"],"links":["1:III.17","1:III.3","1:II.9"],"implied":[],"depth":10,"weight":228,"pos":[1973.5,1794.4,28.2],"landmark":false,"img":{"s":[983,77],"p":[983,1579]}},{"id":"L:3.8","label":"3.8","course":"L","kind":"Korollar","chapter":"3","name":null,"page":21,"title":"Lösbarkeit über die Gaußsche Normalform","note":null,"deps":["L:3.4","L:3.6"],"links":["L:3.4","L:3.6"],"implied":[],"depth":10,"weight":81,"pos":[5144.6,532.2,19.5],"landmark":false,"img":{"s":[983,1831]}},{"id":"2:II.6","label":"II.6","course":"2","kind":"Definition","chapter":"II","name":"Richtungsableitung","page":18,"title":"Richtungsableitung","note":null,"deps":["2:I.4"],"links":["2:I.4"],"implied":[],"depth":10,"weight":85,"pos":[3259.4,5110.6,19.8],"landmark":false,"img":{"s":[983,1482]}},{"id":"2:I.7","label":"I.7","course":"2","kind":"Definition","chapter":"I","name":null,"page":5,"title":"Konvergenz im metrischen Raum","note":null,"deps":["2:I.3","2:I.6","1:III.2"],"links":["2:I.6","1:III.2"],"implied":[{"id":"2:I.3","via":"2:I.6"}],"depth":10,"weight":109,"pos":[2573.6,5066.1,21.7],"landmark":false,"img":{"s":[983,276]}},{"id":"2:I.14","label":"I.14","course":"2","kind":"Definition","chapter":"I","name":null,"page":8,"title":"Dichte Menge","note":null,"deps":["2:I.11"],"links":["2:I.11"],"implied":[],"depth":10,"weight":0,"pos":[2426,5056.6,6],"landmark":false,"img":{"s":[983,255]}},{"id":"2:I.18","label":"I.18","course":"2","kind":"Definition","chapter":"I","name":null,"page":8,"title":"Lipschitz-Stetigkeit","note":null,"deps":["2:I.17"],"links":["2:I.17"],"implied":[],"depth":10,"weight":21,"pos":[2467.7,5027.5,12.9],"landmark":false,"img":{"s":[983,780]}},{"id":"2:I.20","label":"I.20","course":"2","kind":"Satz","chapter":"I","name":null,"page":9,"title":"Stetig ⇔ Urbilder offener Mengen offen","note":null,"deps":["2:I.17","2:I.4"],"links":["2:I.17","2:I.4"],"implied":[],"depth":10,"weight":2,"pos":[2465.5,5080.5,8.1],"landmark":true,"img":{"s":[983,70],"p":[983,287]}},{"id":"2:III.3","label":"III.3","course":"2","kind":"Definition","chapter":"III","name":null,"page":29,"title":"Wegzusammenhang","note":null,"deps":["2:I.17"],"links":["2:I.17"],"implied":[],"depth":10,"weight":7,"pos":[4169.7,5180.1,10],"landmark":false,"img":{"s":[983,357]}},{"id":"L:12.4","label":"12.4","course":"L","kind":"Korollar","chapter":"12","name":null,"page":139,"title":"sign(σ⁻¹) = sign(σ)","note":null,"deps":["L:12.3"],"links":["L:12.3"],"implied":[],"depth":10,"weight":7,"pos":[6349.7,1919,10],"landmark":false,"img":{"s":[983,41],"p":[983,233]}},{"id":"L:5.55","label":"5.55","course":"L","kind":"Definition","chapter":"5","name":null,"page":59,"title":"Invertierbare Matrix","note":null,"deps":["L:5.52"],"links":["L:5.52"],"implied":[],"depth":10,"weight":104,"pos":[5222.2,1225.1,21.3],"landmark":false,"img":{"s":[983,207]}},{"id":"L:18.8","label":"18.8","course":"L","kind":"Definition","chapter":"18","name":null,"page":191,"title":"Symmetrische, hermitesche, positiv definite Matrizen","note":null,"deps":["L:5.59"],"links":["L:5.59"],"implied":[],"depth":10,"weight":19,"pos":[7129.3,1776.4,12.5],"landmark":false,"img":{"s":[983,311]}},{"id":"L:6.9","label":"6.9","course":"L","kind":"Satz","chapter":"6","name":null,"page":79,"title":"Linear abhängig ⇔ ein Vektor ist Kombination der übrigen","note":null,"deps":["L:6.7"],"links":["L:6.7"],"implied":[],"depth":10,"weight":123,"pos":[6502.9,1495.8,22.6],"landmark":false,"img":{"s":[983,99],"p":[983,767]}},{"id":"L:6.10","label":"6.10","course":"L","kind":"Satz","chapter":"6","name":null,"page":80,"title":"Obermengen linear abhängiger Mengen","note":null,"deps":["L:6.7"],"links":["L:6.7"],"implied":[],"depth":10,"weight":130,"pos":[6580.1,1504.4,23.1],"landmark":false,"img":{"s":[983,121],"p":[983,315]}},{"id":"L:6.15","label":"6.15","course":"L","kind":"Definition","chapter":"6","name":null,"page":82,"title":"Elementaroperationen für Vektoren","note":null,"deps":["L:6.13"],"links":["L:6.13"],"implied":[],"depth":10,"weight":0,"pos":[6624.5,1462.4,6],"landmark":false,"img":{"s":[983,191]}},{"id":"L:6.17","label":"6.17","course":"L","kind":"Definition","chapter":"6","name":null,"page":83,"title":"Erzeugendensystem","note":null,"deps":["L:6.13"],"links":["L:6.13"],"implied":[],"depth":10,"weight":220,"pos":[6420.1,1491.8,28.2],"landmark":false,"img":{"s":[983,132]}},{"id":"L:8.4","label":"8.4","course":"L","kind":"Lemma","chapter":"8","name":"Lineare Hülle = UVR","page":95,"title":"Lineare Hülle ist Untervektorraum","note":null,"deps":["L:8.2","L:6.13"],"links":["L:8.2","L:6.13"],"implied":[],"depth":10,"weight":103,"pos":[4644.9,1729.4,21.2],"landmark":false,"img":{"s":[983,66],"p":[983,578]}},{"id":"L:8.5","label":"8.5","course":"L","kind":"Lemma","chapter":"8","name":"Durchschnitt von UVR","page":95,"title":"Durchschnitt von Untervektorräumen","note":null,"deps":["L:8.2"],"links":["L:8.2"],"implied":[],"depth":10,"weight":67,"pos":[4714.3,1746.7,18.3],"landmark":false,"img":{"s":[983,200],"p":[983,142]}},{"id":"L:8.27","label":"8.27","course":"L","kind":"Definition","chapter":"8","name":null,"page":106,"title":"Faktorraum","note":null,"deps":["L:8.26","L:4.24"],"links":["L:8.26","L:4.24"],"implied":[],"depth":10,"weight":13,"pos":[4775.8,1752.4,11.4],"landmark":false,"img":{"s":[983,356]}},{"id":"L:9.12","label":"9.12","course":"L","kind":"Lemma","chapter":"9","name":null,"page":113,"title":"Das Bild ist ein Untervektorraum","note":null,"deps":["L:9.2","L:8.2"],"links":["L:9.2","L:8.2"],"implied":[],"depth":10,"weight":95,"pos":[5411.6,1692.3,20.6],"landmark":false,"img":{"s":[983,68],"p":[983,886]}},{"id":"L:9.7","label":"9.7","course":"L","kind":"Lemma","chapter":"9","name":null,"page":112,"title":"Bilder linear abhängiger Vektoren","note":null,"deps":["L:9.3","L:9.2"],"links":["L:9.3","L:9.2"],"implied":[],"depth":10,"weight":0,"pos":[5362.2,1723.9,6],"landmark":false,"img":{"s":[983,70],"p":[983,211]}},{"id":"L:9.10","label":"9.10","course":"L","kind":"Lemma","chapter":"9","name":null,"page":113,"title":"Der Kern ist ein Untervektorraum","note":null,"deps":["L:9.9","L:8.2"],"links":["L:9.9","L:8.2"],"implied":[],"depth":10,"weight":95,"pos":[5543,1675,20.6],"landmark":false,"img":{"s":[983,139],"p":[983,136]}},{"id":"L:9.11","label":"9.11","course":"L","kind":"Satz","chapter":"9","name":"Kriterium für injektiv","page":113,"title":"Injektiv ⇔ Kern = {0}","note":null,"deps":["L:9.9","L:9.2"],"links":["L:9.9","L:9.2"],"implied":[],"depth":10,"weight":81,"pos":[5343.1,1669.6,19.5],"landmark":false,"img":{"s":[983,68],"p":[983,427]}},{"id":"L:13.1","label":"13.1","course":"L","kind":"Definition","chapter":"13","name":null,"page":150,"title":"Eigenwert, Eigenvektor, Eigenraum","note":null,"deps":["L:9.1","L:9.9"],"links":["L:9.9"],"implied":[{"id":"L:9.1","via":"L:9.9"}],"depth":10,"weight":62,"pos":[6251.5,1811.1,17.8],"landmark":false,"img":{"s":[983,346]}},{"id":"L:9.27","label":"9.27","course":"L","kind":"Lemma","chapter":"9","name":null,"page":120,"title":"Summen linearer Abbildungen sind linear","note":null,"deps":["L:9.26"],"links":["L:9.26"],"implied":[],"depth":10,"weight":83,"pos":[5481.1,1712.3,19.7],"landmark":false,"img":{"s":[983,133],"p":[983,573]}},{"id":"L:17.11","label":"17.11","course":"L","kind":"Definition","chapter":"17","name":null,"page":177,"title":"Jordan-Block","note":null,"deps":["L:17.1"],"links":["L:17.1"],"implied":[],"depth":10,"weight":7,"pos":[6315.9,2396.5,10],"landmark":false,"img":{"s":[983,392]}},{"id":"L:20.6","label":"20.6","course":"L","kind":"Definition","chapter":"20","name":null,"page":245,"title":"Quadratische Form","note":null,"deps":["L:20.1"],"links":["L:20.1"],"implied":[],"depth":10,"weight":15,"pos":[6873,2464.2,11.8],"landmark":false,"img":{"s":[983,194]}},{"id":"L:20.11","label":"20.11","course":"L","kind":"Definition","chapter":"20","name":null,"page":247,"title":"Nullraum einer Bilinearform","note":null,"deps":["L:20.1"],"links":["L:20.1"],"implied":[],"depth":10,"weight":10,"pos":[6921.8,2488.6,10.7],"landmark":false,"img":{"s":[983,101]}},{"id":"L:12.9","label":"12.9","course":"L","kind":"Satz","chapter":"12","name":"Eindeutigkeit","page":140,"title":"Eindeutigkeit der Determinantenfunktion","note":null,"deps":["L:12.7","L:12.3"],"links":["L:12.7","L:12.3"],"implied":[],"depth":10,"weight":89,"pos":[6287.9,1925.5,20.2],"landmark":false,"img":{"s":[983,78],"p":[983,923]}},{"id":"L:21.11","label":"21.11","course":"L","kind":"Satz","chapter":"21","name":"Intrinsische Charakterisierung eines affinen Unterraumes","page":265,"title":"Intrinsische Charakterisierung affiner Unterräume","note":null,"deps":["L:21.7"],"links":["L:21.7"],"implied":[],"depth":10,"weight":2,"pos":[7152.6,1729.2,8.1],"landmark":false,"img":{"s":[983,201],"p":[983,537]}},{"id":"L:21.27","label":"21.27","course":"L","kind":"Definition","chapter":"21","name":null,"page":271,"title":"Parallelität, Teilverhältnis","note":null,"deps":["L:21.7"],"links":["L:21.7"],"implied":[],"depth":10,"weight":1,"pos":[7182.5,1692.1,7.5],"landmark":false,"img":{"s":[983,204]}},{"id":"L:21.15","label":"21.15","course":"L","kind":"Lemma","chapter":"21","name":null,"page":266,"title":"Affin unabhängig ⇔ Differenzen linear unabhängig","note":null,"deps":["L:21.14","L:6.7"],"links":["L:21.14","L:6.7"],"implied":[],"depth":10,"weight":2,"pos":[7225.7,1672.2,8.1],"landmark":false,"img":{"s":[983,116],"p":[983,398]}},{"id":"L:21.21","label":"21.21","course":"L","kind":"Satz","chapter":"21","name":"Allgemeine Form von affinen Abbildungen","page":268,"title":"Affine Abbildung = Translation ∘ linear","note":null,"deps":["L:21.18","L:9.1"],"links":["L:21.18","L:9.1"],"implied":[],"depth":10,"weight":5,"pos":[7004.7,1709.8,9.4],"landmark":false,"img":{"s":[983,354],"p":[983,1028]}},{"id":"L:21.23","label":"21.23","course":"L","kind":"Definition","chapter":"21","name":null,"page":270,"title":"Affinität","note":null,"deps":["L:21.18"],"links":["L:21.18"],"implied":[],"depth":10,"weight":3,"pos":[7221.2,1720.7,8.6],"landmark":false,"img":{"s":[983,104]}},{"id":"1:III.14","label":"III.14","course":"1","kind":"Satz","chapter":"III","name":"Intervallschachtelungsprinzip","page":31,"title":"Intervallschachtelungsprinzip","note":null,"deps":["1:III.13","1:III.10","1:III.7","1:III.8"],"links":["1:III.13","1:III.10","1:III.7","1:III.8"],"implied":[],"depth":11,"weight":473,"pos":[2035.9,1857.1,28.2],"landmark":true,"img":{"s":[983,125],"p":[983,1656]}},{"id":"1:III.12","label":"III.12","course":"1","kind":"Satz","chapter":"III","name":null,"page":30,"title":"e ist irrational","note":null,"deps":["1:III.11","1:II.5","1:III.8"],"links":["1:III.11","1:III.8"],"implied":[{"id":"1:II.5","via":"1:III.11"}],"depth":11,"weight":0,"pos":[1908.7,1780.6,6],"landmark":false,"img":{"s":[983,39],"p":[983,903]}},{"id":"1:III.19","label":"III.19","course":"1","kind":"Lemma","chapter":"III","name":null,"page":36,"title":"limsup und liminf sind Häufungspunkte","note":null,"deps":["1:III.18","1:III.10","1:I.12","1:I.17"],"links":["1:III.18","1:III.10"],"implied":[{"id":"1:I.12","via":"1:III.18"},{"id":"1:I.17","via":"1:III.10"}],"depth":11,"weight":227,"pos":[1850.2,1811.7,28.2],"landmark":false,"img":{"s":[983,74],"p":[983,421]}},{"id":"L:3.9","label":"3.9","course":"L","kind":"Korollar","chapter":"3","name":null,"page":23,"title":"Mehr Unbekannte als Gleichungen ⇒ nichttrivial lösbar","note":null,"deps":["L:3.8"],"links":["L:3.8"],"implied":[],"depth":11,"weight":0,"pos":[5189.7,567.9,6],"landmark":false,"img":{"s":[983,1514]}},{"id":"2:I.8","label":"I.8","course":"2","kind":"Definition","chapter":"I","name":null,"page":5,"title":"Abgeschlossene Menge","note":null,"deps":["2:I.7"],"links":["2:I.7"],"implied":[],"depth":11,"weight":54,"pos":[2470.1,5158.8,17],"landmark":false,"img":{"s":[983,257]}},{"id":"2:I.15","label":"I.15","course":"2","kind":"Definition","chapter":"I","name":null,"page":8,"title":"Kompakte Menge","note":null,"deps":["2:I.7","1:III.16"],"links":["2:I.7","1:III.16"],"implied":[],"depth":11,"weight":74,"pos":[2656.5,5121.2,18.9],"landmark":true,"img":{"s":[983,255]}},{"id":"2:IV.4","label":"IV.4","course":"2","kind":"Definition","chapter":"IV","name":null,"page":61,"title":"Cauchy-Folge, vollständiger metrischer Raum","note":null,"deps":["2:I.7","1:III.22"],"links":["2:I.7","1:III.22"],"implied":[],"depth":11,"weight":52,"pos":[3072.9,5572.1,16.8],"landmark":false,"img":{"s":[983,379]}},{"id":"L:5.56","label":"5.56","course":"L","kind":"Satz","chapter":"5","name":null,"page":59,"title":"GL(n, K) ist eine Gruppe","note":null,"deps":["L:5.52","L:5.55","L:5.9"],"links":["L:5.55"],"implied":[{"id":"L:5.52","via":"L:5.55"},{"id":"L:5.9","via":"L:5.52"}],"depth":11,"weight":35,"pos":[5241.4,1290.5,14.9],"landmark":false,"img":{"s":[983,77],"p":[983,1714]}},{"id":"L:18.48","label":"18.48","course":"L","kind":"Definition","chapter":"18","name":null,"page":213,"title":"Orthogonale und unitäre Matrizen","note":null,"deps":["L:5.55","L:5.59"],"links":["L:5.55","L:5.59"],"implied":[],"depth":11,"weight":38,"pos":[7031.8,1888.1,15.2],"landmark":false,"img":{"s":[983,245]}},{"id":"L:12.8","label":"12.8","course":"L","kind":"Satz","chapter":"12","name":null,"page":140,"title":"Abhängige Vektoren ⇒ Determinante 0","note":null,"deps":["L:12.7","L:6.9"],"links":["L:12.7","L:6.9"],"implied":[],"depth":11,"weight":72,"pos":[6329.2,1983.1,18.7],"landmark":false,"img":{"s":[983,68],"p":[983,572]}},{"id":"L:6.11","label":"6.11","course":"L","kind":"Satz","chapter":"6","name":null,"page":80,"title":"Teilmengen linear unabhängiger Mengen","note":null,"deps":["L:6.10"],"links":["L:6.10"],"implied":[],"depth":11,"weight":112,"pos":[6446.1,1569.7,21.9],"landmark":false,"img":{"s":[983,69],"p":[983,216]}},{"id":"L:6.12","label":"6.12","course":"L","kind":"Satz","chapter":"6","name":null,"page":81,"title":"k+1 Kombinationen von k Vektoren sind abhängig","note":null,"deps":["L:6.10","1:II.3"],"links":["L:6.10","1:II.3"],"implied":[],"depth":11,"weight":103,"pos":[6521.2,1569.4,21.2],"landmark":false,"img":{"s":[983,67],"p":[983,1727]}},{"id":"L:7.1","label":"7.1","course":"L","kind":"Definition","chapter":"7","name":null,"page":85,"title":"Basis","note":null,"deps":["L:6.7","L:6.17"],"links":["L:6.7","L:6.17"],"implied":[],"depth":11,"weight":219,"pos":[4659.7,1874.6,28.2],"landmark":false,"img":{"s":[983,140]}},{"id":"L:8.19","label":"8.19","course":"L","kind":"Lemma","chapter":"8","name":null,"page":103,"title":"Zeilenraum und seine Basis nach Gauß","note":null,"deps":["L:8.4","L:3.8"],"links":["L:8.4","L:3.8"],"implied":[],"depth":11,"weight":79,"pos":[4599.5,1807.5,19.3],"landmark":false,"img":{"s":[983,117],"p":[983,741]}},{"id":"L:8.6","label":"8.6","course":"L","kind":"Satz","chapter":"8","name":null,"page":96,"title":"Lineare Hülle = kleinster Untervektorraum","note":null,"deps":["L:8.4","L:8.5"],"links":["L:8.4","L:8.5"],"implied":[],"depth":11,"weight":64,"pos":[4668,1796.8,18],"landmark":false,"img":{"s":[983,207],"p":[983,179]}},{"id":"L:21.9","label":"21.9","course":"L","kind":"Lemma","chapter":"21","name":null,"page":264,"title":"Durchschnitte affiner Unterräume","note":null,"deps":["L:21.7","L:8.5"],"links":["L:21.7","L:8.5"],"implied":[],"depth":11,"weight":1,"pos":[7016.1,1788.3,7.5],"landmark":false,"img":{"s":[983,312],"p":[983,334]}},{"id":"L:8.28","label":"8.28","course":"L","kind":"Satz","chapter":"8","name":null,"page":106,"title":"Der Faktorraum ist ein Vektorraum","note":null,"deps":["L:8.27","L:6.1"],"links":["L:8.27"],"implied":[{"id":"L:6.1","via":"L:8.27"}],"depth":11,"weight":2,"pos":[4587,1749.4,8.1],"landmark":false,"img":{"s":[983,159],"p":[983,719]}},{"id":"L:9.15","label":"9.15","course":"L","kind":"Definition","chapter":"9","name":null,"page":115,"title":"Kanonische Projektion","note":null,"deps":["L:8.27"],"links":["L:8.27"],"implied":[],"depth":11,"weight":2,"pos":[5393.3,1758,8.1],"landmark":false,"img":{"s":[983,243]}},{"id":"L:9.13","label":"9.13","course":"L","kind":"Lemma","chapter":"9","name":null,"page":114,"title":"Urbilder sind Nebenklassen des Kerns","note":null,"deps":["L:9.10","L:8.27"],"links":["L:9.10","L:8.27"],"implied":[],"depth":11,"weight":6,"pos":[5443,1760.4,9.7],"landmark":false,"img":{"s":[983,231],"p":[983,291]}},{"id":"L:9.8","label":"9.8","course":"L","kind":"Lemma","chapter":"9","name":null,"page":112,"title":"Injektive lineare Abbildungen erhalten Unabhängigkeit","note":null,"deps":["L:9.3","L:9.11"],"links":["L:9.3","L:9.11"],"implied":[],"depth":11,"weight":0,"pos":[5538.4,1733.5,6],"landmark":false,"img":{"s":[983,100],"p":[983,706]}},{"id":"L:13.3","label":"13.3","course":"L","kind":"Satz","chapter":"13","name":null,"page":151,"title":"Eigenvektoren zu verschiedenen Eigenwerten sind unabhängig","note":null,"deps":["L:13.1","L:6.7","1:II.3"],"links":["L:13.1","L:6.7","1:II.3"],"implied":[],"depth":11,"weight":5,"pos":[6263.3,1869.1,9.4],"landmark":false,"img":{"s":[983,69],"p":[983,662]}},{"id":"L:17.2","label":"17.2","course":"L","kind":"Lemma","chapter":"17","name":null,"page":167,"title":"Die Kerne Kₖ sind invariant und wachsend","note":null,"deps":["L:9.10","L:13.1"],"links":["L:9.10","L:13.1"],"implied":[],"depth":11,"weight":12,"pos":[6266.1,2415,11.2],"landmark":false,"img":{"s":[983,141],"p":[983,518]}},{"id":"L:9.28","label":"9.28","course":"L","kind":"Satz","chapter":"9","name":null,"page":120,"title":"Hom(V, W) ist ein Vektorraum","note":null,"deps":["L:9.27","L:6.1"],"links":["L:9.27"],"implied":[{"id":"L:6.1","via":"L:9.27"}],"depth":11,"weight":82,"pos":[5504.1,1779.7,19.6],"landmark":false,"img":{"s":[983,77],"p":[983,269]}},{"id":"L:20.8","label":"20.8","course":"L","kind":"Lemma","chapter":"20","name":"Zusammenhang Bilinearform/Quadratische Form","page":245,"title":"Polarisierung: Bilinearform aus quadratischer Form","note":null,"deps":["L:20.6"],"links":["L:20.6"],"implied":[],"depth":11,"weight":9,"pos":[6897.9,2550.1,10.5],"landmark":false,"img":{"s":[983,361],"p":[983,625]}},{"id":"L:21.38","label":"21.38","course":"L","kind":"Definition","chapter":"21","name":null,"page":275,"title":"Quadrik","note":null,"deps":["L:20.6"],"links":["L:20.6"],"implied":[],"depth":11,"weight":5,"pos":[7158.2,1821.9,9.4],"landmark":false,"img":{"s":[983,834]}},{"id":"L:12.10","label":"12.10","course":"L","kind":"Satz","chapter":"12","name":"Existenz","page":141,"title":"Existenz: Leibniz-Formel","note":null,"deps":["L:12.9","L:12.1","L:12.3"],"links":["L:12.9"],"implied":[{"id":"L:12.1","via":"L:12.9"},{"id":"L:12.3","via":"L:12.9"}],"depth":11,"weight":88,"pos":[6258.9,1991.6,20.1],"landmark":true,"img":{"s":[983,148],"p":[983,2637]}},{"id":"L:21.12","label":"21.12","course":"L","kind":"Definition","chapter":"21","name":null,"page":266,"title":"Affine Hülle","note":null,"deps":["L:21.11"],"links":["L:21.11"],"implied":[],"depth":11,"weight":1,"pos":[7037.2,1746.3,7.5],"landmark":false,"img":{"s":[983,222]}},{"id":"L:21.16","label":"21.16","course":"L","kind":"Definition","chapter":"21","name":null,"page":266,"title":"Affine Basis, Koordinaten","note":null,"deps":["L:21.15"],"links":["L:21.15"],"implied":[],"depth":11,"weight":1,"pos":[7108,1823.9,7.5],"landmark":false,"img":{"s":[983,481]}},{"id":"L:21.29","label":"21.29","course":"L","kind":"Lemma","chapter":"21","name":null,"page":271,"title":"Affine Abbildungen sind parallelen- und teilverhältnistreu","note":null,"deps":["L:21.27","L:21.21"],"links":["L:21.27","L:21.21"],"implied":[],"depth":11,"weight":0,"pos":[7249,1776.6,6],"landmark":false,"img":{"s":[983,119],"p":[983,242]}},{"id":"L:21.25","label":"21.25","course":"L","kind":"Satz","chapter":"21","name":null,"page":270,"title":"Affinitäten bilden eine Gruppe","note":null,"deps":["L:21.23","L:21.21","L:5.9"],"links":["L:21.23","L:21.21"],"implied":[{"id":"L:5.9","via":"L:21.23"}],"depth":11,"weight":2,"pos":[6981.2,1755.9,8.1],"landmark":false,"img":{"s":[983,77],"p":[983,462]}},{"id":"1:III.15","label":"III.15","course":"1","kind":"Satz","chapter":"III","name":null,"page":32,"title":"Existenz der n-ten Wurzel","note":null,"deps":["1:III.14","1:III.7","1:III.8","1:I.8"],"links":["1:III.14"],"implied":[{"id":"1:III.7","via":"1:III.14"},{"id":"1:III.8","via":"1:III.14"},{"id":"1:I.8","via":"1:III.14"}],"depth":12,"weight":471,"pos":[1920.6,1865.3,28.2],"landmark":false,"img":{"s":[983,113],"p":[983,2534]}},{"id":"1:IV.6","label":"IV.6","course":"1","kind":"Satz","chapter":"IV","name":null,"page":42,"title":"ℝ ist überabzählbar","note":null,"deps":["1:III.14"],"links":["1:III.14"],"implied":[],"depth":12,"weight":0,"pos":[793.5,2268.1,6],"landmark":false,"img":{"s":[983,40],"p":[983,774]}},{"id":"1:III.20","label":"III.20","course":"1","kind":"Satz","chapter":"III","name":"Bolzano-Weierstrass","page":36,"title":"Bolzano-Weierstraß","note":"Kein eigener Beweis: direkte Folge von Lemma III.19","deps":["1:III.19"],"links":["1:III.19"],"implied":[],"depth":12,"weight":209,"pos":[1839.4,1899,27.7],"landmark":true,"img":{"s":[983,750]}},{"id":"2:I.24","label":"I.24","course":"2","kind":"Definition","chapter":"I","name":null,"page":10,"title":"Zusammenhängender Raum","note":null,"deps":["2:I.4","2:I.8"],"links":["2:I.4","2:I.8"],"implied":[],"depth":12,"weight":21,"pos":[2516.4,5199.8,12.9],"landmark":false,"img":{"s":[983,201]}},{"id":"2:IV.5","label":"IV.5","course":"2","kind":"Satz","chapter":"IV","name":"Fixpunktsatz von Banach","page":61,"title":"Fixpunktsatz von Banach","note":null,"deps":["2:IV.4","2:I.1","1:II.5"],"links":["2:IV.4","1:II.5"],"implied":[{"id":"2:I.1","via":"2:IV.4"}],"depth":12,"weight":39,"pos":[3077.3,5649.7,15.4],"landmark":true,"img":{"s":[983,276],"p":[983,976]}},{"id":"L:10.7","label":"10.7","course":"L","kind":"Definition","chapter":"10","name":null,"page":130,"title":"Äquivalente Matrizen","note":null,"deps":["L:5.56"],"links":["L:5.56"],"implied":[],"depth":12,"weight":2,"pos":[5493.1,2245.3,8.1],"landmark":false,"img":{"s":[983,77]}},{"id":"L:7.3","label":"7.3","course":"L","kind":"Satz","chapter":"7","name":"Basis = erzeugend + minimal","page":86,"title":"Basis ⇔ minimales Erzeugendensystem","note":null,"deps":["L:7.1","L:6.9"],"links":["L:7.1","L:6.9"],"implied":[],"depth":12,"weight":0,"pos":[4778.1,1989.9,6],"landmark":false,"img":{"s":[983,99],"p":[983,665]}},{"id":"L:7.4","label":"7.4","course":"L","kind":"Satz","chapter":"7","name":"Basis = linear unabhängig + maximal","page":86,"title":"Basis ⇔ maximal linear unabhängig","note":null,"deps":["L:7.1","L:6.9"],"links":["L:7.1","L:6.9"],"implied":[],"depth":12,"weight":120,"pos":[4814.6,1941.7,22.4],"landmark":false,"img":{"s":[983,396]}},{"id":"L:7.10","label":"7.10","course":"L","kind":"Satz","chapter":"7","name":"Anzahl Basiselemente","page":88,"title":"Alle Basen sind gleich groß","note":null,"deps":["L:6.12","L:7.1"],"links":["L:6.12","L:7.1"],"implied":[],"depth":12,"weight":102,"pos":[4595.4,1924.3,21.1],"landmark":true,"img":{"s":[983,77],"p":[983,204]}},{"id":"L:7.14","label":"7.14","course":"L","kind":"Definition","chapter":"7","name":null,"page":89,"title":"Basisdarstellung","note":null,"deps":["L:7.1"],"links":["L:7.1"],"implied":[],"depth":12,"weight":196,"pos":[4733.1,1943,27],"landmark":false,"img":{"s":[983,205]}},{"id":"L:8.20","label":"8.20","course":"L","kind":"Lemma","chapter":"8","name":null,"page":103,"title":"Spaltenraum und Treppenstufen","note":null,"deps":["L:8.19"],"links":["L:8.19"],"implied":[],"depth":12,"weight":78,"pos":[4727.2,1832.7,19.2],"landmark":false,"img":{"s":[983,258],"p":[983,1372]}},{"id":"L:8.8","label":"8.8","course":"L","kind":"Definition","chapter":"8","name":null,"page":96,"title":"Summe von Untervektorräumen","note":null,"deps":["L:8.6"],"links":["L:8.6"],"implied":[],"depth":12,"weight":63,"pos":[4558.7,1863.5,17.9],"landmark":false,"img":{"s":[983,157]}},{"id":"L:9.17","label":"9.17","course":"L","kind":"Satz","chapter":"9","name":"Homomorphiesatz","page":115,"title":"Homomorphiesatz","note":null,"deps":["L:9.13","L:9.15","L:8.28"],"links":["L:9.13","L:9.15","L:8.28"],"implied":[],"depth":12,"weight":1,"pos":[5427.4,1811.8,7.5],"landmark":true,"img":{"s":[983,287],"p":[983,682]}},{"id":"L:16.1","label":"16.1","course":"L","kind":"Definition","chapter":"16","name":null,"page":163,"title":"Einsetzen von Endomorphismen in Polynome","note":null,"deps":["L:5.60","L:9.28"],"links":["L:5.60","L:9.28"],"implied":[],"depth":12,"weight":2,"pos":[5850,2648,8.1],"landmark":false,"img":{"s":[983,434]}},{"id":"2:V.23","label":"V.23","course":"2","kind":"Definition","chapter":"V","name":null,"page":91,"title":"Differentialform vom Grad 1","note":null,"deps":["2:I.4","L:9.28"],"links":["2:I.4","L:9.28"],"implied":[],"depth":12,"weight":3,"pos":[4887.9,5229.8,8.6],"landmark":false,"img":{"s":[983,905]}},{"id":"L:21.41","label":"21.41","course":"L","kind":"Lemma","chapter":"21","name":"Quadrik als Begriff der affinen Geometrie","page":276,"title":"Affine Bilder von Quadriken sind Quadriken","note":null,"deps":["L:21.38","L:21.21"],"links":["L:21.38","L:21.21"],"implied":[],"depth":12,"weight":2,"pos":[7049.2,1833.1,8.1],"landmark":false,"img":{"s":[983,141],"p":[983,764]}},{"id":"L:12.11","label":"12.11","course":"L","kind":"Definition","chapter":"12","name":null,"page":143,"title":"Determinante einer Matrix","note":null,"deps":["L:12.10"],"links":["L:12.10"],"implied":[],"depth":12,"weight":87,"pos":[6302.9,2048.7,20],"landmark":false,"img":{"s":[983,490]}},{"id":"L:21.13","label":"21.13","course":"L","kind":"Lemma","chapter":"21","name":null,"page":266,"title":"Affine Hülle = kleinster affiner Unterraum","note":null,"deps":["L:21.11","L:21.9","L:21.12"],"links":["L:21.9","L:21.12"],"implied":[{"id":"L:21.11","via":"L:21.12"}],"depth":12,"weight":0,"pos":[7132.9,1862,6],"landmark":false,"img":{"s":[983,35],"p":[983,131]}},{"id":"1:IV.7","label":"IV.7","course":"1","kind":"Definition","chapter":"IV","name":null,"page":42,"title":"Euklidische Norm","note":null,"deps":["1:III.15"],"links":["1:III.15"],"implied":[],"depth":13,"weight":470,"pos":[876.1,2326.8,28.2],"landmark":false,"img":{"s":[983,265]}},{"id":"1:III.21","label":"III.21","course":"1","kind":"Satz","chapter":"III","name":null,"page":36,"title":"Konvergenz ⇔ liminf = limsup","note":null,"deps":["1:III.19","1:III.20","1:III.17","1:III.8"],"links":["1:III.20","1:III.8"],"implied":[{"id":"1:III.19","via":"1:III.20"},{"id":"1:III.17","via":"1:III.19"}],"depth":13,"weight":0,"pos":[2025.9,1922.6,6],"landmark":false,"img":{"s":[983,207],"p":[983,92]}},{"id":"1:III.24","label":"III.24","course":"1","kind":"Satz","chapter":"III","name":null,"page":37,"title":"Cauchy ⇒ konvergent","note":null,"deps":["1:III.22","1:III.20","1:III.5","1:III.2","1:I.10"],"links":["1:III.22","1:III.20","1:I.10"],"implied":[{"id":"1:III.5","via":"1:III.20"},{"id":"1:III.2","via":"1:III.20"}],"depth":13,"weight":167,"pos":[1964.6,1938.8,25.4],"landmark":true,"img":{"s":[983,37],"p":[983,2866]}},{"id":"L:7.5","label":"7.5","course":"L","kind":"Satz","chapter":"7","name":"Basisergänzungssatz","page":87,"title":"Basisergänzungssatz","note":null,"deps":["L:7.4","L:6.11"],"links":["L:7.4","L:6.11"],"implied":[],"depth":13,"weight":111,"pos":[4610,2029.2,21.8],"landmark":true,"img":{"s":[983,99],"p":[983,200]}},{"id":"L:7.11","label":"7.11","course":"L","kind":"Definition","chapter":"7","name":null,"page":88,"title":"Dimension","note":null,"deps":["L:7.10"],"links":["L:7.10"],"implied":[],"depth":13,"weight":101,"pos":[4680.2,2003,21.1],"landmark":false,"img":{"s":[983,197]}},{"id":"L:7.15","label":"7.15","course":"L","kind":"Satz","chapter":"7","name":"Eindeutige Basisdarstellung","page":89,"title":"Basisdarstellung ist eindeutig","note":null,"deps":["L:7.14","L:6.7"],"links":["L:7.14"],"implied":[{"id":"L:6.7","via":"L:7.14"}],"depth":13,"weight":192,"pos":[4835.4,2020.2,26.8],"landmark":false,"img":{"s":[983,101],"p":[983,499]}},{"id":"L:20.3","label":"20.3","course":"L","kind":"Definition","chapter":"20","name":null,"page":244,"title":"Matrix einer Bilinearform","note":null,"deps":["L:20.1","L:7.14"],"links":["L:20.1","L:7.14"],"implied":[],"depth":13,"weight":0,"pos":[6826.9,2633.5,6],"landmark":false,"img":{"s":[983,71]}},{"id":"L:8.9","label":"8.9","course":"L","kind":"Satz","chapter":"8","name":"Charakterisierung Summe","page":96,"title":"Charakterisierung der Summe","note":null,"deps":["L:8.8","L:8.2"],"links":["L:8.8"],"implied":[{"id":"L:8.2","via":"L:8.8"}],"depth":13,"weight":3,"pos":[4665.5,1943.1,8.6],"landmark":false,"img":{"s":[983,101],"p":[983,232]}},{"id":"L:8.10","label":"8.10","course":"L","kind":"Definition","chapter":"8","name":null,"page":97,"title":"Direkte Summe","note":null,"deps":["L:8.8"],"links":["L:8.8"],"implied":[],"depth":13,"weight":60,"pos":[4777.1,1880.2,17.6],"landmark":false,"img":{"s":[983,157]}},{"id":"L:9.18","label":"9.18","course":"L","kind":"Korollar","chapter":"9","name":"Isomorphiesatz","page":116,"title":"Isomorphiesatz","note":null,"deps":["L:9.17","L:9.12"],"links":["L:9.17","L:9.12"],"implied":[],"depth":13,"weight":0,"pos":[5463.3,1865.6,6],"landmark":false,"img":{"s":[983,329]}},{"id":"L:21.42","label":"21.42","course":"L","kind":"Definition","chapter":"21","name":null,"page":276,"title":"Affine Äquivalenz von Quadriken","note":null,"deps":["L:21.41","L:21.25"],"links":["L:21.41","L:21.25"],"implied":[],"depth":13,"weight":1,"pos":[7123.8,1906.6,7.5],"landmark":false,"img":{"s":[983,5625]}},{"id":"L:12.14","label":"12.14","course":"L","kind":"Satz","chapter":"12","name":null,"page":145,"title":"det Aᵀ = det A","note":null,"deps":["L:12.11","L:12.4"],"links":["L:12.11","L:12.4"],"implied":[],"depth":13,"weight":6,"pos":[6277.5,2104.9,9.7],"landmark":false,"img":{"s":[983,36],"p":[983,451]}},{"id":"L:12.16","label":"12.16","course":"L","kind":"Satz","chapter":"12","name":"Determinanten-Multiplikationssatz","page":146,"title":"Determinanten-Multiplikationssatz","note":null,"deps":["L:12.7","L:12.9","L:12.11"],"links":["L:12.11"],"implied":[{"id":"L:12.7","via":"L:12.9"},{"id":"L:12.9","via":"L:12.11"}],"depth":13,"weight":85,"pos":[6336.9,2120.8,19.8],"landmark":true,"img":{"s":[983,100],"p":[983,586]}},{"id":"1:IV.9","label":"IV.9","course":"1","kind":"Definition","chapter":"IV","name":null,"page":43,"title":"Skalarprodukt","note":null,"deps":["1:IV.7","L:18.1"],"links":["1:IV.7","L:18.1"],"implied":[],"depth":14,"weight":284,"pos":[777.1,2353.5,28.2],"landmark":false,"img":{"s":[983,234]}},{"id":"1:IV.12","label":"IV.12","course":"1","kind":"Definition","chapter":"IV","name":null,"page":45,"title":"Konvergenz im ℝⁿ, Kugeln","note":null,"deps":["1:IV.7","1:III.2"],"links":["1:IV.7"],"implied":[{"id":"1:III.2","via":"1:IV.7"}],"depth":14,"weight":367,"pos":[930.7,2396.4,28.2],"landmark":false,"img":{"s":[983,766]}},{"id":"1:IV.C","label":"IV.C","course":"1","kind":"Definition","chapter":"IV","name":null,"page":49,"title":"Komplexe Zahlen ℂ","note":"Im Skript ohne Nummer eingeführt (S. 50)","deps":["1:I.1","1:IV.7"],"links":["1:IV.7"],"implied":[{"id":"1:I.1","via":"1:IV.7"}],"depth":14,"weight":329,"pos":[688.9,2359.8,28.2],"landmark":false,"img":{"s":[983,617]}},{"id":"1:VI.13","label":"VI.13","course":"1","kind":"Definition","chapter":"VI","name":null,"page":78,"title":"Grenzwert für x → ±∞","note":null,"deps":["1:IV.7"],"links":["1:IV.7"],"implied":[],"depth":14,"weight":0,"pos":[1999.1,2631.1,6],"landmark":false,"img":{"s":[983,540]}},{"id":"1:IX.3","label":"IX.3","course":"1","kind":"Definition","chapter":"IX","name":null,"page":111,"title":"Supremumsnorm","note":null,"deps":["1:I.11","1:IV.7"],"links":["1:IV.7"],"implied":[{"id":"1:I.11","via":"1:IV.7"}],"depth":14,"weight":127,"pos":[2964.9,2872.1,22.9],"landmark":false,"img":{"s":[983,203]}},{"id":"L:7.6","label":"7.6","course":"L","kind":"Korollar","chapter":"7","name":null,"page":87,"title":"Endlich erzeugt ⇒ endliche Basis","note":null,"deps":["L:7.5"],"links":["L:7.5"],"implied":[],"depth":14,"weight":0,"pos":[4548,2064.8,6],"landmark":false,"img":{"s":[983,68],"p":[983,135]}},{"id":"L:7.8","label":"7.8","course":"L","kind":"Satz","chapter":"7","name":"Eine Basis existiert immer","page":87,"title":"Jeder Vektorraum hat eine Basis","note":"Für unendliche Dimension mit dem Zornschen Lemma","deps":["L:7.5","L:4.20"],"links":["L:7.5","L:4.20"],"implied":[],"depth":14,"weight":0,"pos":[4661.8,2059.1,6],"landmark":false,"img":{"s":[983,35],"p":[983,104]}},{"id":"L:7.13","label":"7.13","course":"L","kind":"Satz","chapter":"7","name":null,"page":88,"title":"n+1 Vektoren abhängig, n unabhängige sind Basis","note":null,"deps":["L:7.11","L:6.12","L:7.4"],"links":["L:7.11","L:7.4"],"implied":[{"id":"L:6.12","via":"L:7.11"}],"depth":14,"weight":89,"pos":[4719.7,2064.7,20.2],"landmark":false,"img":{"s":[983,146],"p":[983,911]}},{"id":"L:8.21","label":"8.21","course":"L","kind":"Definition","chapter":"8","name":null,"page":104,"title":"Zeilenrang und Spaltenrang","note":null,"deps":["L:7.11","L:8.4"],"links":["L:7.11","L:8.4"],"implied":[],"depth":14,"weight":78,"pos":[4553.2,1983.2,19.2],"landmark":false,"img":{"s":[983,150]}},{"id":"L:9.19","label":"9.19","course":"L","kind":"Definition","chapter":"9","name":null,"page":116,"title":"Rang einer linearen Abbildung","note":null,"deps":["L:9.12","L:7.11"],"links":["L:9.12","L:7.11"],"implied":[],"depth":14,"weight":87,"pos":[5422.6,1927.8,20],"landmark":false,"img":{"s":[983,122]}},{"id":"L:7.16","label":"7.16","course":"L","kind":"Definition","chapter":"7","name":null,"page":90,"title":"Komponentenvektor","note":null,"deps":["L:7.15"],"links":["L:7.15"],"implied":[],"depth":14,"weight":172,"pos":[4667.6,2122.6,25.7],"landmark":false,"img":{"s":[983,174]}},{"id":"L:9.6","label":"9.6","course":"L","kind":"Satz","chapter":"9","name":"lineare Fortsetzung","page":111,"title":"Lineare Fortsetzung von einer Basis","note":null,"deps":["L:9.1","L:7.15"],"links":["L:9.1","L:7.15"],"implied":[],"depth":14,"weight":170,"pos":[5500.1,1931,25.6],"landmark":false,"img":{"s":[983,149],"p":[983,935]}},{"id":"L:8.11","label":"8.11","course":"L","kind":"Satz","chapter":"8","name":"Charakterisierung direkte Summe","page":97,"title":"Direkt ⇔ Zerlegung eindeutig","note":null,"deps":["L:8.10","L:8.9"],"links":["L:8.10","L:8.9"],"implied":[],"depth":14,"weight":0,"pos":[4629.5,1972.6,6],"landmark":false,"img":{"s":[983,133],"p":[983,380]}},{"id":"L:8.13","label":"8.13","course":"L","kind":"Satz","chapter":"8","name":"Komplement","page":97,"title":"Existenz eines Komplements","note":null,"deps":["L:8.10","L:7.5"],"links":["L:8.10","L:7.5"],"implied":[],"depth":14,"weight":0,"pos":[4738.9,2009.8,6],"landmark":false,"img":{"s":[983,101],"p":[983,167]}},{"id":"1:IV.10","label":"IV.10","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":43,"title":"Eigenschaften des Skalarprodukts","note":null,"deps":["1:IV.9"],"links":["1:IV.9"],"implied":[],"depth":15,"weight":280,"pos":[604,2428.6,28.2],"landmark":false,"img":{"s":[983,220],"p":[983,133]}},{"id":"1:IV.14","label":"IV.14","course":"1","kind":"Definition","chapter":"IV","name":null,"page":46,"title":"Häufungspunkt einer Menge","note":null,"deps":["1:IV.12","1:II.9"],"links":["1:IV.12","1:II.9"],"implied":[],"depth":15,"weight":219,"pos":[764.9,2441.1,28.2],"landmark":false,"img":{"s":[983,175]}},{"id":"1:IV.16","label":"IV.16","course":"1","kind":"Definition","chapter":"IV","name":null,"page":47,"title":"Offen, abgeschlossen","note":null,"deps":["1:IV.12"],"links":["1:IV.12"],"implied":[],"depth":15,"weight":185,"pos":[844.8,2407.6,26.4],"landmark":false,"img":{"s":[983,1212]}},{"id":"1:IV.19","label":"IV.19","course":"1","kind":"Definition","chapter":"IV","name":null,"page":49,"title":"Folgenkompakt","note":null,"deps":["1:III.16","1:IV.12"],"links":["1:III.16","1:IV.12"],"implied":[],"depth":15,"weight":164,"pos":[713,2512.9,25.2],"landmark":false,"img":{"s":[983,132]}},{"id":"1:VI.1","label":"VI.1","course":"1","kind":"Definition","chapter":"VI","name":null,"page":72,"title":"Stetigkeit (ε-δ)","note":null,"deps":["1:IV.7","1:IV.12"],"links":["1:IV.12"],"implied":[{"id":"1:IV.7","via":"1:IV.12"}],"depth":15,"weight":232,"pos":[2079.4,2692,28.2],"landmark":false,"img":{"s":[983,1917]}},{"id":"1:IV.21","label":"IV.21","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":50,"title":"Rechenregeln für die Konjugation","note":null,"deps":["1:IV.C"],"links":["1:IV.C"],"implied":[],"depth":15,"weight":96,"pos":[684,2440.6,20.7],"landmark":false,"img":{"s":[983,237],"p":[983,414]}},{"id":"1:IV.23","label":"IV.23","course":"1","kind":"Definition","chapter":"IV","name":null,"page":52,"title":"Polynom","note":null,"deps":["1:IV.C"],"links":["1:IV.C"],"implied":[],"depth":15,"weight":70,"pos":[894.5,2466.4,18.5],"landmark":false,"img":{"s":[983,301]}},{"id":"1:IX.1","label":"IX.1","course":"1","kind":"Definition","chapter":"IX","name":null,"page":110,"title":"Punktweise und gleichmäßige Konvergenz","note":null,"deps":["1:III.2","1:II.7","1:IV.C"],"links":["1:IV.C"],"implied":[{"id":"1:III.2","via":"1:IV.C"},{"id":"1:II.7","via":"1:III.2"}],"depth":15,"weight":104,"pos":[2903,2916.4,21.3],"landmark":false,"img":{"s":[983,1830]}},{"id":"L:18.3","label":"18.3","course":"L","kind":"Definition","chapter":"18","name":null,"page":189,"title":"Hermitesche Form","note":null,"deps":["L:6.1","1:IV.C"],"links":["L:6.1","1:IV.C"],"implied":[],"depth":15,"weight":95,"pos":[7161.4,1632.2,20.6],"landmark":false,"img":{"s":[983,293]}},{"id":"2:V.27","label":"V.27","course":"2","kind":"Definition","chapter":"V","name":null,"page":94,"title":"Komplex differenzierbar, holomorph","note":null,"deps":["2:I.4","1:IV.C"],"links":["2:I.4","1:IV.C"],"implied":[],"depth":15,"weight":8,"pos":[4861.3,5273.1,10.2],"landmark":false,"img":{"s":[983,1019]}},{"id":"1:X.3","label":"X.3","course":"1","kind":"Definition","chapter":"X","name":"Riemann-Integral","page":118,"title":"Riemann-Integral","note":null,"deps":["1:X.2","1:IX.3"],"links":["1:X.2","1:IX.3"],"implied":[],"depth":15,"weight":122,"pos":[3262.3,2571.9,22.6],"landmark":false,"img":{"s":[983,911]}},{"id":"L:8.15","label":"8.15","course":"L","kind":"Satz","chapter":"8","name":null,"page":98,"title":"dim U ≤ dim V","note":null,"deps":["L:8.1","L:7.10","L:7.13"],"links":["L:8.1","L:7.13"],"implied":[{"id":"L:7.10","via":"L:7.13"}],"depth":15,"weight":85,"pos":[4593.2,2100.9,19.8],"landmark":false,"img":{"s":[983,99],"p":[983,371]}},{"id":"L:13.4","label":"13.4","course":"L","kind":"Korollar","chapter":"13","name":null,"page":151,"title":"Höchstens n Eigenwerte, Eigenräume bilden direkte Summe","note":null,"deps":["L:13.3","L:7.13","L:8.10"],"links":["L:13.3","L:7.13","L:8.10"],"implied":[],"depth":15,"weight":4,"pos":[6158.8,2077,9],"landmark":false,"img":{"s":[983,1617]}},{"id":"L:8.22","label":"8.22","course":"L","kind":"Satz","chapter":"8","name":"Rang","page":105,"title":"Zeilenrang = Spaltenrang","note":null,"deps":["L:8.19","L:8.20","L:8.21"],"links":["L:8.20","L:8.21"],"implied":[{"id":"L:8.19","via":"L:8.20"}],"depth":15,"weight":77,"pos":[4788.7,2082.6,19.2],"landmark":true,"img":{"s":[983,160],"p":[983,136]}},{"id":"L:9.21","label":"9.21","course":"L","kind":"Satz","chapter":"9","name":null,"page":117,"title":"Dimensionsformel: dim V = dim Kern + Rang","note":null,"deps":["L:9.19","L:7.5","L:7.4","L:9.10"],"links":["L:9.19","L:7.5","L:9.10"],"implied":[{"id":"L:7.4","via":"L:7.5"}],"depth":15,"weight":84,"pos":[5453.3,1992.6,19.7],"landmark":true,"img":{"s":[983,192],"p":[983,1234]}},{"id":"L:7.19","label":"7.19","course":"L","kind":"Satz","chapter":"7","name":"Basiswechsel: Übergangsmatrizen","page":92,"title":"Übergangsmatrizen sind invers zueinander","note":null,"deps":["L:7.16","L:5.55"],"links":["L:7.16","L:5.55"],"implied":[],"depth":15,"weight":52,"pos":[4790.4,2150.6,16.8],"landmark":false,"img":{"s":[983,131],"p":[983,800]}},{"id":"L:10.1","label":"10.1","course":"L","kind":"Lemma","chapter":"10","name":"und Definition","page":125,"title":"Abbildungsmatrix einer linearen Abbildung","note":null,"deps":["L:9.6","L:9.26","L:5.49","L:7.16"],"links":["L:9.6","L:9.26","L:5.49","L:7.16"],"implied":[],"depth":15,"weight":154,"pos":[5427.9,2390.9,24.6],"landmark":false,"img":{"s":[983,238],"p":[983,1149]}},{"id":"1:IV.11","label":"IV.11","course":"1","kind":"Satz","chapter":"IV","name":"Cauchy-Schwarz Ungleichung","page":44,"title":"Cauchy-Schwarz-Ungleichung","note":null,"deps":["1:IV.10","1:IV.9","1:IV.7"],"links":["1:IV.10"],"implied":[{"id":"1:IV.9","via":"1:IV.10"},{"id":"1:IV.7","via":"1:IV.10"}],"depth":16,"weight":279,"pos":[808.3,2574.5,28.2],"landmark":true,"img":{"s":[983,175],"p":[983,1460]}},{"id":"1:IV.15","label":"IV.15","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":46,"title":"Häufungspunkt über Folgen","note":null,"deps":["1:IV.14","1:IV.12"],"links":["1:IV.14"],"implied":[{"id":"1:IV.12","via":"1:IV.14"}],"depth":16,"weight":166,"pos":[653.3,2569.9,25.3],"landmark":false,"img":{"s":[983,89],"p":[983,649]}},{"id":"1:VI.10","label":"VI.10","course":"1","kind":"Definition","chapter":"VI","name":null,"page":77,"title":"Grenzwert einer Funktion","note":null,"deps":["1:IV.14","1:IV.7"],"links":["1:IV.14"],"implied":[{"id":"1:IV.7","via":"1:IV.14"}],"depth":16,"weight":215,"pos":[1980.4,2778.5,28],"landmark":false,"img":{"s":[983,285]}},{"id":"1:IV.17","label":"IV.17","course":"1","kind":"Satz","chapter":"IV","name":null,"page":47,"title":"Offen ⇔ Komplement abgeschlossen","note":null,"deps":["1:IV.16"],"links":["1:IV.16"],"implied":[],"depth":16,"weight":40,"pos":[829.8,2480,15.5],"landmark":false,"img":{"s":[983,76],"p":[983,564]}},{"id":"1:IV.18","label":"IV.18","course":"1","kind":"Satz","chapter":"IV","name":null,"page":48,"title":"Offene Mengen bilden eine Topologie","note":null,"deps":["1:IV.16"],"links":["1:IV.16"],"implied":[],"depth":16,"weight":54,"pos":[640.6,2496.6,17],"landmark":false,"img":{"s":[983,268],"p":[983,817]}},{"id":"1:VI.2","label":"VI.2","course":"1","kind":"Definition","chapter":"VI","name":null,"page":73,"title":"Lipschitz-Stetigkeit","note":null,"deps":["1:VI.1","1:IV.7"],"links":["1:VI.1"],"implied":[{"id":"1:IV.7","via":"1:VI.1"}],"depth":16,"weight":0,"pos":[2035.9,2742.8,6],"landmark":false,"img":{"s":[983,2074]}},{"id":"1:VI.3","label":"VI.3","course":"1","kind":"Satz","chapter":"VI","name":null,"page":75,"title":"Folgenstetigkeit ⇔ Stetigkeit","note":null,"deps":["1:VI.1","1:IV.12"],"links":["1:VI.1"],"implied":[{"id":"1:IV.12","via":"1:VI.1"}],"depth":16,"weight":207,"pos":[2090.5,2779.2,27.6],"landmark":true,"img":{"s":[983,208],"p":[983,726]}},{"id":"1:VI.6","label":"VI.6","course":"1","kind":"Lemma","chapter":"VI","name":null,"page":76,"title":"Stetig und ≠ 0 bleibt lokal ≠ 0","note":null,"deps":["1:VI.1","1:I.10"],"links":["1:VI.1"],"implied":[{"id":"1:I.10","via":"1:VI.1"}],"depth":16,"weight":141,"pos":[1995.5,2696,23.8],"landmark":false,"img":{"s":[983,167],"p":[983,248]}},{"id":"3:V.16","label":"V.16","course":"3","kind":"Definition","chapter":"V","name":null,"page":68,"title":"Träger, Räume C_c⁰(Ω)","note":null,"deps":["2:I.11","2:I.15","1:VI.1"],"links":["2:I.11","2:I.15","1:VI.1"],"implied":[],"depth":16,"weight":14,"pos":[4705.8,8117.2,11.6],"landmark":false,"img":{"s":[983,497]}},{"id":"1:IV.22","label":"IV.22","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":51,"title":"Betrag komplexer Zahlen","note":null,"deps":["1:IV.21","1:IV.C","1:IV.7"],"links":["1:IV.21"],"implied":[{"id":"1:IV.C","via":"1:IV.21"},{"id":"1:IV.7","via":"1:IV.21"}],"depth":16,"weight":95,"pos":[728.8,2589.2,20.6],"landmark":false,"img":{"s":[983,232],"p":[983,599]}},{"id":"1:IV.24","label":"IV.24","course":"1","kind":"Satz","chapter":"IV","name":"Polynomdivision","page":52,"title":"Polynomdivision","note":null,"deps":["1:IV.23"],"links":["1:IV.23"],"implied":[],"depth":16,"weight":8,"pos":[780.4,2509.8,10.2],"landmark":false,"img":{"s":[983,185],"p":[983,596]}},{"id":"1:IV.28","label":"IV.28","course":"1","kind":"Satz","chapter":"IV","name":"Fundamentalsatz der Algebra","page":54,"title":"Fundamentalsatz der Algebra","note":"Beweis in Analysis II (Satz V.18)","deps":["1:IV.23"],"links":["1:IV.23"],"implied":[],"depth":16,"weight":52,"pos":[870.9,2529.5,16.8],"landmark":true,"img":{"s":[983,172]}},{"id":"1:IX.4","label":"IX.4","course":"1","kind":"Satz","chapter":"IX","name":null,"page":112,"title":"Gleichmäßig ⇔ ‖fₙ − f‖∞ → 0","note":null,"deps":["1:IX.1","1:IX.3"],"links":["1:IX.1","1:IX.3"],"implied":[],"depth":16,"weight":98,"pos":[3040.4,3027,20.8],"landmark":false,"img":{"s":[983,195],"p":[983,472]}},{"id":"L:18.4","label":"18.4","course":"L","kind":"Lemma","chapter":"18","name":"Elementare Eigenschaften einer hermiteschen Form","page":189,"title":"Eigenschaften hermitescher Formen","note":null,"deps":["L:18.3"],"links":["L:18.3"],"implied":[],"depth":16,"weight":0,"pos":[7046.2,1687.1,6],"landmark":false,"img":{"s":[983,240],"p":[983,312]}},{"id":"L:18.5","label":"18.5","course":"L","kind":"Definition","chapter":"18","name":null,"page":190,"title":"Positiv definit, unitärer Raum","note":null,"deps":["L:18.3","L:18.1"],"links":["L:18.3","L:18.1"],"implied":[],"depth":16,"weight":93,"pos":[7092.4,1722.9,20.5],"landmark":false,"img":{"s":[983,320]}},{"id":"2:V.31","label":"V.31","course":"2","kind":"Definition","chapter":"V","name":null,"page":97,"title":"Komplexe Stammfunktion","note":null,"deps":["2:V.27"],"links":["2:V.27"],"implied":[],"depth":16,"weight":1,"pos":[5005,5355.9,7.5],"landmark":false,"img":{"s":[983,257]}},{"id":"1:X.4","label":"X.4","course":"1","kind":"Satz","chapter":"X","name":null,"page":119,"title":"Linearität des Integrals","note":null,"deps":["1:X.3"],"links":["1:X.3"],"implied":[],"depth":16,"weight":8,"pos":[3386.7,2619.5,10.2],"landmark":false,"img":{"s":[983,195],"p":[983,639]}},{"id":"1:X.5","label":"X.5","course":"1","kind":"Lemma","chapter":"X","name":null,"page":120,"title":"Endlich viele Punkte ändern das Integral nicht","note":null,"deps":["1:X.3","1:II.3"],"links":["1:X.3","1:II.3"],"implied":[],"depth":16,"weight":98,"pos":[3337.3,2580.3,20.8],"landmark":false,"img":{"s":[983,84],"p":[983,575]}},{"id":"1:X.6","label":"X.6","course":"1","kind":"Lemma","chapter":"X","name":null,"page":120,"title":"Additivität über Teilintervalle","note":null,"deps":["1:X.3","1:IX.3"],"links":["1:X.3"],"implied":[{"id":"1:IX.3","via":"1:X.3"}],"depth":16,"weight":99,"pos":[3275.7,2646.2,20.9],"landmark":false,"img":{"s":[983,173],"p":[983,691]}},{"id":"1:X.8","label":"X.8","course":"1","kind":"Satz","chapter":"X","name":null,"page":122,"title":"∣∫f∣ ≤ ∣I∣·‖f‖∞","note":null,"deps":["1:X.3","1:IX.3"],"links":["1:X.3"],"implied":[{"id":"1:IX.3","via":"1:X.3"}],"depth":16,"weight":100,"pos":[3390.6,2682.6,21],"landmark":false,"img":{"s":[983,120],"p":[983,192]}},{"id":"1:X.12","label":"X.12","course":"1","kind":"Satz","chapter":"X","name":null,"page":124,"title":"Monotonie des Integrals","note":null,"deps":["1:X.3"],"links":["1:X.3"],"implied":[],"depth":16,"weight":11,"pos":[3339.5,2644.1,11],"landmark":false,"img":{"s":[983,121],"p":[983,192]}},{"id":"1:X.14","label":"X.14","course":"1","kind":"Satz","chapter":"X","name":null,"page":125,"title":"Ober- und Unterintegral","note":null,"deps":["1:X.3","1:I.11","1:II.3"],"links":["1:X.3","1:II.3"],"implied":[{"id":"1:I.11","via":"1:X.3"}],"depth":16,"weight":1,"pos":[3201.8,2558.2,7.5],"landmark":false,"img":{"s":[983,160],"p":[983,447]}},{"id":"L:8.17","label":"8.17","course":"L","kind":"Satz","chapter":"8","name":"Dimensionssatz für UVR","page":100,"title":"Dimensionssatz für Untervektorräume","note":null,"deps":["L:8.15","L:7.5","L:8.9"],"links":["L:8.15","L:7.5","L:8.9"],"implied":[],"depth":16,"weight":1,"pos":[4732.7,2125.4,7.5],"landmark":true,"img":{"s":[983,128],"p":[983,1756]}},{"id":"L:17.3","label":"17.3","course":"L","kind":"Lemma","chapter":"17","name":null,"page":167,"title":"Die Kernkette wird stationär","note":null,"deps":["L:17.2","L:8.15"],"links":["L:17.2","L:8.15"],"implied":[],"depth":16,"weight":11,"pos":[6235.7,2727.6,11],"landmark":false,"img":{"s":[983,165],"p":[983,471]}},{"id":"L:8.23","label":"8.23","course":"L","kind":"Korollar","chapter":"8","name":null,"page":105,"title":"Rang der Transponierten","note":null,"deps":["L:8.22","L:5.59"],"links":["L:8.22","L:5.59"],"implied":[],"depth":16,"weight":1,"pos":[4612.3,2157,7.5],"landmark":false,"img":{"s":[983,36]}},{"id":"L:9.22","label":"9.22","course":"L","kind":"Satz","chapter":"9","name":null,"page":118,"title":"Injektiv/surjektiv über den Rang","note":null,"deps":["L:9.11","L:9.21","L:8.15"],"links":["L:9.11","L:9.21","L:8.15"],"implied":[],"depth":16,"weight":78,"pos":[5404.8,2044.5,19.2],"landmark":false,"img":{"s":[983,141],"p":[983,211]}},{"id":"L:7.20","label":"7.20","course":"L","kind":"Satz","chapter":"7","name":"Basiswechsel: Vektor-Komponenten","page":93,"title":"Komponenten beim Basiswechsel","note":null,"deps":["L:7.19"],"links":["L:7.19"],"implied":[],"depth":16,"weight":0,"pos":[4643.8,2207.5,6],"landmark":false,"img":{"s":[983,221],"p":[983,1133]}},{"id":"L:10.9","label":"10.9","course":"L","kind":"Definition","chapter":"10","name":null,"page":131,"title":"Ähnliche Matrizen","note":null,"deps":["L:5.56","L:7.19"],"links":["L:5.56","L:7.19"],"implied":[],"depth":16,"weight":11,"pos":[5505.8,2465.2,11],"landmark":false,"img":{"s":[983,1200]}},{"id":"L:10.3","label":"10.3","course":"L","kind":"Satz","chapter":"10","name":null,"page":126,"title":"Matrix der Verkettung = Produkt der Matrizen","note":null,"deps":["L:10.1","L:5.50"],"links":["L:10.1","L:5.50"],"implied":[],"depth":16,"weight":74,"pos":[5443.9,2464.7,18.9],"landmark":false,"img":{"s":[983,169],"p":[983,496]}},{"id":"L:10.5","label":"10.5","course":"L","kind":"Satz","chapter":"10","name":null,"page":128,"title":"Duale Abbildung und Transponierte","note":null,"deps":["L:10.1","L:9.28","L:5.59"],"links":["L:10.1","L:9.28","L:5.59"],"implied":[],"depth":16,"weight":0,"pos":[5482,2422.4,6],"landmark":false,"img":{"s":[983,1159]}},{"id":"L:10.6","label":"10.6","course":"L","kind":"Satz","chapter":"10","name":null,"page":129,"title":"Rang der Abbildung = Rang der Matrix","note":null,"deps":["L:10.1","L:8.22","L:9.19"],"links":["L:10.1","L:8.22","L:9.19"],"implied":[],"depth":16,"weight":3,"pos":[5384.4,2462.4,8.6],"landmark":false,"img":{"s":[983,123],"p":[983,2125]}},{"id":"L:11.1","label":"11.1","course":"L","kind":"Lemma","chapter":"11","name":null,"page":133,"title":"LGS als lineare Abbildung","note":null,"deps":["L:9.12","L:10.1","L:3.1"],"links":["L:9.12","L:10.1","L:3.1"],"implied":[],"depth":16,"weight":7,"pos":[4678.1,2510.5,10],"landmark":false,"img":{"s":[983,166],"p":[983,685]}},{"id":"L:15.1","label":"15.1","course":"L","kind":"Definition","chapter":"15","name":null,"page":161,"title":"Trigonalisierbar","note":null,"deps":["L:10.1"],"links":["L:10.1"],"implied":[],"depth":16,"weight":4,"pos":[4870.3,2899.3,9],"landmark":false,"img":{"s":[983,100]}},{"id":"1:IV.8","label":"IV.8","course":"1","kind":"Satz","chapter":"IV","name":null,"page":43,"title":"Eigenschaften der Norm","note":null,"deps":["1:IV.7","1:IV.11","1:III.15"],"links":["1:IV.11"],"implied":[{"id":"1:IV.7","via":"1:IV.11"},{"id":"1:III.15","via":"1:IV.7"}],"depth":17,"weight":273,"pos":[904.2,2599,28.2],"landmark":false,"img":{"s":[983,251],"p":[983,482]}},{"id":"1:VI.11","label":"VI.11","course":"1","kind":"Lemma","chapter":"VI","name":null,"page":77,"title":"Grenzwert = Funktionswert ⇔ stetig","note":null,"deps":["1:VI.10","1:VI.1"],"links":["1:VI.10","1:VI.1"],"implied":[],"depth":17,"weight":141,"pos":[2114.8,2858.9,23.8],"landmark":false,"img":{"s":[983,188],"p":[983,216]}},{"id":"1:VI.12","label":"VI.12","course":"1","kind":"Definition","chapter":"VI","name":null,"page":78,"title":"Uneigentlicher Grenzwert ±∞","note":null,"deps":["1:VI.10"],"links":["1:VI.10"],"implied":[],"depth":17,"weight":0,"pos":[1942.4,2832.4,6],"landmark":false,"img":{"s":[983,210]}},{"id":"1:VII.6","label":"VII.6","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":83,"title":"Einseitige Grenzwerte monotoner Funktionen","note":null,"deps":["1:VII.5","1:I.17","1:VI.10"],"links":["1:VII.5","1:VI.10"],"implied":[{"id":"1:I.17","via":"1:VI.10"}],"depth":17,"weight":23,"pos":[1339.2,3310.5,13.2],"landmark":false,"img":{"s":[983,118],"p":[983,218]}},{"id":"1:VIII.1","label":"VIII.1","course":"1","kind":"Definition","chapter":"VIII","name":null,"page":93,"title":"Ableitung","note":null,"deps":["1:VI.10"],"links":["1:VI.10"],"implied":[],"depth":17,"weight":195,"pos":[2260,3154.6,26.9],"landmark":false,"img":{"s":[983,872]}},{"id":"1:XI.8","label":"XI.8","course":"1","kind":"Definition","chapter":"XI","name":"Uneigentliches Integral","page":133,"title":"Uneigentliches Integral","note":null,"deps":["1:X.3","1:VI.10"],"links":["1:X.3","1:VI.10"],"implied":[],"depth":17,"weight":2,"pos":[3734.8,3297.5,8.1],"landmark":false,"img":{"s":[983,365]}},{"id":"2:I.9","label":"I.9","course":"2","kind":"Satz","chapter":"I","name":null,"page":5,"title":"Offen ⇔ Komplement abgeschlossen","note":"Beweis: Verweis auf Ana I, Satz IV.17","deps":["2:I.4","2:I.8","1:IV.17"],"links":["2:I.4","2:I.8","1:IV.17"],"implied":[],"depth":17,"weight":2,"pos":[2549,5158,8.1],"landmark":false,"img":{"s":[983,85],"p":[983,42]}},{"id":"2:I.5","label":"I.5","course":"2","kind":"Satz","chapter":"I","name":null,"page":4,"title":"Offene Mengen bilden eine Topologie","note":"Beweis: Verweis auf Ana I, Satz IV.18","deps":["2:I.4","1:IV.18"],"links":["2:I.4","1:IV.18"],"implied":[],"depth":17,"weight":1,"pos":[2514.1,5051.8,7.5],"landmark":false,"img":{"s":[983,230],"p":[983,42]}},{"id":"3:I.14","label":"I.14","course":"3","kind":"Lemma","chapter":"I","name":null,"page":10,"title":"Messbarkeitskriterien für numerische Funktionen","note":null,"deps":["3:I.13","3:I.12","1:IV.16","1:IV.18"],"links":["3:I.13","3:I.12","1:IV.18"],"implied":[{"id":"1:IV.16","via":"1:IV.18"}],"depth":17,"weight":51,"pos":[3024.9,7559.7,16.7],"landmark":false,"img":{"s":[983,325],"p":[983,1181]}},{"id":"1:VI.4","label":"VI.4","course":"1","kind":"Satz","chapter":"VI","name":null,"page":75,"title":"Verkettung stetiger Funktionen","note":null,"deps":["1:VI.3"],"links":["1:VI.3"],"implied":[],"depth":17,"weight":0,"pos":[1974.9,2862,6],"landmark":false,"img":{"s":[983,117],"p":[983,338]}},{"id":"1:VI.14","label":"VI.14","course":"1","kind":"Satz","chapter":"VI","name":null,"page":78,"title":"Grenzwert über Folgen","note":"Beweis nur \"analog zu Satz VI.3\"","deps":["1:VI.10","1:IV.15","1:VI.3"],"links":["1:VI.10","1:IV.15","1:VI.3"],"implied":[],"depth":17,"weight":163,"pos":[2035.3,2843.5,25.2],"landmark":false,"img":{"s":[983,208],"p":[983,121]}},{"id":"1:VII.1","label":"VII.1","course":"1","kind":"Satz","chapter":"VII","name":"Zwischenwertsatz","page":81,"title":"Zwischenwertsatz","note":null,"deps":["1:I.12","1:I.17","1:VI.3","1:III.8"],"links":["1:VI.3"],"implied":[{"id":"1:I.12","via":"1:VI.3"},{"id":"1:I.17","via":"1:VI.3"},{"id":"1:III.8","via":"1:VI.3"}],"depth":17,"weight":36,"pos":[1317.2,3254.4,15],"landmark":true,"img":{"s":[983,211],"p":[983,442]}},{"id":"1:VII.3","label":"VII.3","course":"1","kind":"Satz","chapter":"VII","name":"Satz vom Maximum","page":82,"title":"Satz vom Maximum","note":null,"deps":["1:IV.19","1:VI.3","1:I.17"],"links":["1:IV.19","1:VI.3"],"implied":[{"id":"1:I.17","via":"1:IV.19"}],"depth":17,"weight":136,"pos":[1270.6,3307.3,23.5],"landmark":true,"img":{"s":[983,168],"p":[983,448]}},{"id":"1:X.10","label":"X.10","course":"1","kind":"Satz","chapter":"X","name":null,"page":123,"title":"Stetig auf kompakt ⇒ gleichmäßig stetig","note":null,"deps":["1:IV.19","1:VI.3"],"links":["1:IV.19","1:VI.3"],"implied":[],"depth":17,"weight":100,"pos":[3176.4,2693.9,21],"landmark":false,"img":{"s":[983,143],"p":[983,524]}},{"id":"2:I.19","label":"I.19","course":"2","kind":"Satz","chapter":"I","name":null,"page":9,"title":"Folgenkriterium für Stetigkeit","note":"Kein eigener Beweis: wie Ana I, Satz VI.3","deps":["2:I.17","2:I.7","1:VI.3"],"links":["2:I.17","2:I.7","1:VI.3"],"implied":[],"depth":17,"weight":68,"pos":[2516.2,5109.6,18.4],"landmark":false,"img":{"s":[983,343]}},{"id":"1:VI.7","label":"VI.7","course":"1","kind":"Satz","chapter":"VI","name":null,"page":76,"title":"Summe, Produkt, Quotient stetiger Funktionen","note":null,"deps":["1:VI.3","1:III.7","1:VI.6"],"links":["1:VI.3","1:VI.6"],"implied":[{"id":"1:III.7","via":"1:VI.3"}],"depth":17,"weight":1,"pos":[2151.4,2807.2,7.5],"landmark":false,"img":{"s":[983,248],"p":[983,359]}},{"id":"1:IV.25","label":"IV.25","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":52,"title":"Höchstens n Nullstellen","note":null,"deps":["1:IV.24","1:II.3"],"links":["1:IV.24","1:II.3"],"implied":[],"depth":17,"weight":7,"pos":[771.9,2634.5,10],"landmark":false,"img":{"s":[983,74],"p":[983,376]}},{"id":"L:13.8","label":"13.8","course":"L","kind":"Satz","chapter":"13","name":"Fundamentalsatz der Algebra","page":153,"title":"Fundamentalsatz der Algebra","note":"Im LA-Skript ohne Beweis; bewiesen in Analysis II (Satz V.18)","deps":["L:13.5","1:IV.28"],"links":["L:13.5","1:IV.28"],"implied":[],"depth":17,"weight":48,"pos":[6249.2,1745,16.4],"landmark":false,"img":{"s":[983,124]}},{"id":"L:18.7","label":"18.7","course":"L","kind":"Definition","chapter":"18","name":null,"page":190,"title":"Gramsche Matrix eines Skalarprodukts","note":null,"deps":["L:18.5","L:7.14"],"links":["L:18.5","L:7.14"],"implied":[],"depth":17,"weight":16,"pos":[7018.9,1970.8,12],"landmark":false,"img":{"s":[983,1271]}},{"id":"L:18.12","label":"18.12","course":"L","kind":"Satz","chapter":"18","name":"Cauchy-Schwarz Ungleichung","page":193,"title":"Cauchy-Schwarz-Ungleichung","note":null,"deps":["L:18.5"],"links":["L:18.5"],"implied":[],"depth":17,"weight":22,"pos":[7072.4,1785.3,13],"landmark":true,"img":{"s":[983,192],"p":[983,697]}},{"id":"L:18.25","label":"18.25","course":"L","kind":"Definition","chapter":"18","name":null,"page":200,"title":"Orthogonal","note":null,"deps":["L:18.5"],"links":["L:18.5"],"implied":[],"depth":17,"weight":72,"pos":[7192.4,1772.6,18.7],"landmark":false,"img":{"s":[983,99]}},{"id":"L:19.1","label":"19.1","course":"L","kind":"Definition","chapter":"19","name":null,"page":218,"title":"Adjungierte Abbildung","note":null,"deps":["L:18.5","L:9.1"],"links":["L:18.5","L:9.1"],"implied":[],"depth":17,"weight":44,"pos":[7066.7,2306.6,15.9],"landmark":false,"img":{"s":[983,333]}},{"id":"1:X.7","label":"X.7","course":"1","kind":"Lemma","chapter":"X","name":null,"page":121,"title":"Treppenfunktionen sind integrierbar","note":null,"deps":["1:X.5","1:X.6"],"links":["1:X.5","1:X.6"],"implied":[],"depth":17,"weight":97,"pos":[3247.3,2714.3,20.8],"landmark":false,"img":{"s":[983,210],"p":[983,1297]}},{"id":"1:X.9","label":"X.9","course":"1","kind":"Satz","chapter":"X","name":null,"page":122,"title":"Integral und gleichmäßige Konvergenz","note":null,"deps":["1:X.8","1:X.3","1:IX.4","1:III.24"],"links":["1:X.8","1:IX.4","1:III.24"],"implied":[{"id":"1:X.3","via":"1:X.8"}],"depth":17,"weight":97,"pos":[3320.3,2704.9,20.8],"landmark":false,"img":{"s":[983,158],"p":[983,620]}},{"id":"2:III.35","label":"III.35","course":"2","kind":"Lemma","chapter":"III","name":null,"page":55,"title":"Fundamentallemma der Variationsrechnung","note":null,"deps":["1:X.12","1:VI.6"],"links":["1:X.12","1:VI.6"],"implied":[],"depth":17,"weight":1,"pos":[4225.1,4999.4,7.5],"landmark":false,"img":{"s":[983,189],"p":[983,994]}},{"id":"L:8.18","label":"8.18","course":"L","kind":"Korollar","chapter":"8","name":null,"page":101,"title":"Dimension direkter Summen","note":null,"deps":["L:8.17","L:8.10"],"links":["L:8.17","L:8.10"],"implied":[],"depth":17,"weight":0,"pos":[4590.9,2197.2,6],"landmark":false,"img":{"s":[983,1443]}},{"id":"L:17.4","label":"17.4","course":"L","kind":"Definition","chapter":"17","name":null,"page":168,"title":"Hauptvektor, Hauptraum","note":null,"deps":["L:17.3"],"links":["L:17.3"],"implied":[],"depth":17,"weight":0,"pos":[6300,2800.9,6],"landmark":false,"img":{"s":[983,681]}},{"id":"L:17.6","label":"17.6","course":"L","kind":"Lemma","chapter":"17","name":null,"page":169,"title":"Hauptraum und Bild ergänzen sich direkt","note":null,"deps":["L:17.3","L:9.21","L:8.10"],"links":["L:17.3","L:9.21","L:8.10"],"implied":[],"depth":17,"weight":9,"pos":[6219.9,2784.1,10.5],"landmark":false,"img":{"s":[983,178],"p":[983,796]}},{"id":"L:9.23","label":"9.23","course":"L","kind":"Satz","chapter":"9","name":null,"page":118,"title":"Gleiche Dimension ⇔ isomorph","note":null,"deps":["L:9.22","L:9.6"],"links":["L:9.22","L:9.6"],"implied":[],"depth":17,"weight":77,"pos":[5494.4,2085,19.2],"landmark":false,"img":{"s":[983,67],"p":[983,414]}},{"id":"L:14.1","label":"14.1","course":"L","kind":"Definition","chapter":"14","name":null,"page":156,"title":"Diagonalisierbar","note":null,"deps":["L:10.9"],"links":["L:10.9"],"implied":[],"depth":17,"weight":4,"pos":[5459.2,2794.2,9],"landmark":false,"img":{"s":[983,326]}},{"id":"L:10.8","label":"10.8","course":"L","kind":"Satz","chapter":"10","name":null,"page":130,"title":"Normalform bezüglich Äquivalenz","note":null,"deps":["L:10.7","L:10.6","L:4.22"],"links":["L:10.7","L:10.6","L:4.22"],"implied":[],"depth":17,"weight":0,"pos":[5517.1,2512.9,6],"landmark":false,"img":{"s":[983,319],"p":[983,1142]}},{"id":"L:11.2","label":"11.2","course":"L","kind":"Satz","chapter":"11","name":"Lösbarkeitskriterium","page":134,"title":"Lösbarkeitskriterium Rang A = Rang (A∣b)","note":null,"deps":["L:11.1","L:8.15","L:8.22"],"links":["L:11.1","L:8.15","L:8.22"],"implied":[],"depth":17,"weight":0,"pos":[4607.5,2584,6],"landmark":true,"img":{"s":[983,67],"p":[983,554]}},{"id":"L:11.5","label":"11.5","course":"L","kind":"Satz","chapter":"11","name":null,"page":135,"title":"Lösungsmenge = Nebenklasse des Kerns","note":null,"deps":["L:9.13","L:11.1"],"links":["L:9.13","L:11.1"],"implied":[],"depth":17,"weight":3,"pos":[4653.5,2591.2,8.6],"landmark":false,"img":{"s":[983,501]}},{"id":"L:11.8","label":"11.8","course":"L","kind":"Satz","chapter":"11","name":null,"page":136,"title":"Homogenes LGS: Lösungsraum der Dimension n − Rang A","note":null,"deps":["L:9.21","L:10.6","L:11.1"],"links":["L:9.21","L:10.6","L:11.1"],"implied":[],"depth":17,"weight":1,"pos":[4715.6,2592.7,7.5],"landmark":false,"img":{"s":[983,133]}},{"id":"1:IV.13","label":"IV.13","course":"1","kind":"Satz","chapter":"IV","name":null,"page":45,"title":"Konvergenz ⇔ koordinatenweise Konvergenz","note":null,"deps":["1:IV.12","1:IV.8","1:III.2","1:III.5","1:III.22"],"links":["1:IV.12","1:IV.8","1:III.22"],"implied":[{"id":"1:III.2","via":"1:IV.12"},{"id":"1:III.5","via":"1:IV.12"}],"depth":18,"weight":270,"pos":[838.1,2657.8,28.2],"landmark":false,"img":{"s":[983,113],"p":[983,523]}},{"id":"1:IX.2","label":"IX.2","course":"1","kind":"Satz","chapter":"IX","name":null,"page":111,"title":"Gleichmäßiger Limes stetiger Funktionen ist stetig","note":null,"deps":["1:IX.1","1:VI.1","1:IV.8"],"links":["1:IX.1","1:VI.1","1:IV.8"],"implied":[],"depth":18,"weight":23,"pos":[2947.4,3138.6,13.2],"landmark":false,"img":{"s":[983,79],"p":[983,372]}},{"id":"1:VIII.3","label":"VIII.3","course":"1","kind":"Definition","chapter":"VIII","name":null,"page":94,"title":"Differenzierbar auf I, Ableitungsfunktion","note":null,"deps":["1:VIII.1"],"links":["1:VIII.1"],"implied":[],"depth":18,"weight":125,"pos":[2322.2,3207.5,22.8],"landmark":false,"img":{"s":[983,1181]}},{"id":"2:II.1","label":"II.1","course":"2","kind":"Definition","chapter":"II","name":null,"page":13,"title":"Partielle Ableitung","note":null,"deps":["2:I.4","1:VIII.1"],"links":["2:I.4","1:VIII.1"],"implied":[],"depth":18,"weight":103,"pos":[3404.6,5088,21.2],"landmark":false,"img":{"s":[983,707]}},{"id":"2:I.12","label":"I.12","course":"2","kind":"Satz","chapter":"I","name":null,"page":7,"title":"Eigenschaften von Innerem, Abschluss, Rand","note":null,"deps":["2:I.11","2:I.9","2:I.4"],"links":["2:I.11","2:I.9"],"implied":[{"id":"2:I.4","via":"2:I.9"}],"depth":18,"weight":0,"pos":[2468.8,5235.2,6],"landmark":false,"img":{"s":[983,354],"p":[983,530]}},{"id":"2:I.10","label":"I.10","course":"2","kind":"Lemma","chapter":"I","name":null,"page":5,"title":"Abgeschlossene Mengen: Vereinigung, Durchschnitt","note":null,"deps":["2:I.5","2:I.9"],"links":["2:I.5","2:I.9"],"implied":[],"depth":18,"weight":0,"pos":[2510.1,5250.3,6],"landmark":false,"img":{"s":[983,202],"p":[983,1216]}},{"id":"3:I.15","label":"I.15","course":"3","kind":"Lemma","chapter":"I","name":null,"page":11,"title":"{f < g} und {f ≤ g} sind messbar","note":null,"deps":["3:I.14","1:I.20"],"links":["3:I.14","1:I.20"],"implied":[],"depth":18,"weight":47,"pos":[3075.4,7600.6,16.3],"landmark":false,"img":{"s":[983,99],"p":[983,572]}},{"id":"3:I.16","label":"I.16","course":"3","kind":"Satz","chapter":"I","name":null,"page":12,"title":"inf, sup, liminf, limsup messbarer Funktionen","note":null,"deps":["3:I.14","1:III.19"],"links":["3:I.14","1:III.19"],"implied":[],"depth":18,"weight":48,"pos":[3021.2,7635.9,16.4],"landmark":false,"img":{"s":[983,136],"p":[983,636]}},{"id":"1:VI.15","label":"VI.15","course":"1","kind":"Satz","chapter":"VI","name":null,"page":79,"title":"Rechenregeln für Grenzwerte von Funktionen","note":"Beweis wird den Lesenden überlassen","deps":["1:VI.14","1:III.7","1:III.8","1:VI.3"],"links":["1:VI.14"],"implied":[{"id":"1:III.7","via":"1:VI.14"},{"id":"1:III.8","via":"1:VI.14"},{"id":"1:VI.3","via":"1:VI.14"}],"depth":18,"weight":160,"pos":[2062.9,2920.8,25],"landmark":false,"img":{"s":[983,1631]}},{"id":"1:XI.9","label":"XI.9","course":"1","kind":"Lemma","chapter":"XI","name":null,"page":133,"title":"Cauchy-Kriterium für uneigentliche Integrale","note":null,"deps":["1:XI.8","1:III.24","1:VI.14"],"links":["1:XI.8","1:III.24","1:VI.14"],"implied":[],"depth":18,"weight":0,"pos":[3683.1,3343.9,6],"landmark":false,"img":{"s":[983,158],"p":[983,2547]}},{"id":"1:VII.2","label":"VII.2","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":82,"title":"Stetiges Bild eines Intervalls ist ein Intervall","note":null,"deps":["1:VII.1","1:I.11"],"links":["1:VII.1"],"implied":[{"id":"1:I.11","via":"1:VII.1"}],"depth":18,"weight":31,"pos":[1232.5,3365.8,14.4],"landmark":false,"img":{"s":[983,92],"p":[983,337]}},{"id":"2:I.23","label":"I.23","course":"2","kind":"Satz","chapter":"I","name":null,"page":10,"title":"Stetig auf kompakt ⇒ gleichmäßig stetig","note":"Beweis: wie Ana I, Satz X.10","deps":["2:I.15","2:I.17","1:X.10"],"links":["2:I.15","2:I.17","1:X.10"],"implied":[],"depth":18,"weight":18,"pos":[2704.4,5187.4,12.4],"landmark":false,"img":{"s":[983,64],"p":[983,41]}},{"id":"2:I.21","label":"I.21","course":"2","kind":"Satz","chapter":"I","name":null,"page":9,"title":"Stetige Bilder kompakter Mengen","note":null,"deps":["2:I.15","2:I.19"],"links":["2:I.15","2:I.19"],"implied":[],"depth":18,"weight":14,"pos":[2648.6,5191.4,11.6],"landmark":false,"img":{"s":[983,320],"p":[983,249]}},{"id":"2:I.22","label":"I.22","course":"2","kind":"Satz","chapter":"I","name":null,"page":10,"title":"Satz vom Maximum im metrischen Raum","note":"Beweis: wie Ana I, Satz VII.3","deps":["2:I.15","2:I.19","1:VII.3"],"links":["2:I.15","2:I.19","1:VII.3"],"implied":[],"depth":18,"weight":44,"pos":[2576.8,5207.1,15.9],"landmark":false,"img":{"s":[983,65],"p":[983,371]}},{"id":"2:I.25","label":"I.25","course":"2","kind":"Lemma","chapter":"I","name":null,"page":10,"title":"Zusammenhang ⇔ lokal konstant ist konstant","note":null,"deps":["2:I.24","2:I.19"],"links":["2:I.24","2:I.19"],"implied":[],"depth":18,"weight":20,"pos":[2595.9,5264.7,12.7],"landmark":false,"img":{"s":[983,273],"p":[983,732]}},{"id":"1:VI.8","label":"VI.8","course":"1","kind":"Lemma","chapter":"VI","name":null,"page":77,"title":"C⁰ ist ein Vektorraum","note":"Kein eigener Beweis: direkte Folgerung aus Satz VI.7","deps":["1:VI.7"],"links":["1:VI.7"],"implied":[],"depth":18,"weight":0,"pos":[2125.9,2919.7,6],"landmark":false,"img":{"s":[983,173]}},{"id":"1:IV.26","label":"IV.26","course":"1","kind":"Satz","chapter":"IV","name":"Identitätssatz für Polynome","page":53,"title":"Identitätssatz für Polynome","note":null,"deps":["1:IV.25"],"links":["1:IV.25"],"implied":[],"depth":18,"weight":5,"pos":[719.4,2653.6,9.4],"landmark":false,"img":{"s":[983,266],"p":[983,110]}},{"id":"L:18.9","label":"18.9","course":"L","kind":"Satz","chapter":"18","name":"Beschreibung aller Skalarprodukte","page":192,"title":"Alle Skalarprodukte über positiv definite Matrizen","note":null,"deps":["L:18.7","L:18.8"],"links":["L:18.7","L:18.8"],"implied":[],"depth":18,"weight":0,"pos":[7135.7,2034.9,6],"landmark":false,"img":{"s":[983,190],"p":[983,818]}},{"id":"L:18.10","label":"18.10","course":"L","kind":"Satz","chapter":"18","name":null,"page":192,"title":"Transformation der Gramschen Matrix","note":null,"deps":["L:18.7","L:7.19"],"links":["L:18.7","L:7.19"],"implied":[],"depth":18,"weight":0,"pos":[6950,2117.6,6],"landmark":false,"img":{"s":[983,203]}},{"id":"L:18.15","label":"18.15","course":"L","kind":"Satz","chapter":"18","name":null,"page":194,"title":"Skalarprodukt induziert eine Norm","note":null,"deps":["L:18.12","L:18.14"],"links":["L:18.12","L:18.14"],"implied":[],"depth":18,"weight":19,"pos":[7242.7,1868.3,12.5],"landmark":false,"img":{"s":[983,158],"p":[983,681]}},{"id":"L:18.28","label":"18.28","course":"L","kind":"Definition","chapter":"18","name":null,"page":201,"title":"Orthogonale und orthonormale Mengen","note":null,"deps":["L:18.25"],"links":["L:18.25"],"implied":[],"depth":18,"weight":69,"pos":[6988,1839,18.5],"landmark":false,"img":{"s":[983,276]}},{"id":"L:18.35","label":"18.35","course":"L","kind":"Definition","chapter":"18","name":null,"page":206,"title":"Orthogonalkomplement","note":null,"deps":["L:18.25"],"links":["L:18.25"],"implied":[],"depth":18,"weight":43,"pos":[7183.5,1880.4,15.8],"landmark":false,"img":{"s":[983,131]}},{"id":"L:19.5","label":"19.5","course":"L","kind":"Definition","chapter":"19","name":null,"page":220,"title":"Selbstadjungierter Endomorphismus","note":null,"deps":["L:19.1"],"links":["L:19.1"],"implied":[],"depth":18,"weight":35,"pos":[7160.1,2377.8,14.9],"landmark":false,"img":{"s":[983,189]}},{"id":"L:9.29","label":"9.29","course":"L","kind":"Satz","chapter":"9","name":null,"page":120,"title":"dim Hom(V, W) = dim V · dim W","note":null,"deps":["L:9.6","L:9.23","L:9.28"],"links":["L:9.23","L:9.28"],"implied":[{"id":"L:9.6","via":"L:9.23"}],"depth":18,"weight":75,"pos":[5455.9,2144.9,19],"landmark":false,"img":{"s":[983,183],"p":[983,2812]}},{"id":"L:14.3","label":"14.3","course":"L","kind":"Satz","chapter":"14","name":"1. Kriterium für Diagonalisierbarkeit eines Endomorphismus","page":156,"title":"1. Kriterium: Basis aus Eigenvektoren","note":null,"deps":["L:14.1","L:13.3","L:13.4","L:10.1"],"links":["L:14.1","L:13.4","L:10.1"],"implied":[{"id":"L:13.3","via":"L:13.4"}],"depth":18,"weight":3,"pos":[5501.7,2835.8,8.6],"landmark":false,"img":{"s":[983,318],"p":[983,822]}},{"id":"L:11.6","label":"11.6","course":"L","kind":"Satz","chapter":"11","name":null,"page":136,"title":"Lösung = spezielle + homogene Lösung","note":null,"deps":["L:11.5"],"links":["L:11.5"],"implied":[],"depth":18,"weight":1,"pos":[4612.1,2669.7,7.5],"landmark":false,"img":{"s":[983,384]}},{"id":"L:11.7","label":"11.7","course":"L","kind":"Korollar","chapter":"11","name":null,"page":136,"title":"Eindeutig lösbar ⇔ homogen nur trivial","note":null,"deps":["L:11.5","L:9.11"],"links":["L:11.5","L:9.11"],"implied":[],"depth":18,"weight":0,"pos":[4657.4,2652.1,6],"landmark":false,"img":{"s":[983,585]}},{"id":"1:IV.20","label":"IV.20","course":"1","kind":"Satz","chapter":"IV","name":null,"page":49,"title":"Folgenkompakt ⇔ beschränkt und abgeschlossen","note":null,"deps":["1:IV.19","1:IV.16","1:IV.13","1:III.20","1:III.4"],"links":["1:IV.19","1:IV.16","1:IV.13","1:III.20","1:III.4"],"implied":[],"depth":19,"weight":157,"pos":[883.5,2729.8,24.8],"landmark":true,"img":{"s":[983,208],"p":[983,1993]}},{"id":"1:V.1","label":"V.1","course":"1","kind":"Definition","chapter":"V","name":null,"page":56,"title":"Reihe, Konvergenz einer Reihe","note":null,"deps":["1:III.1","1:III.2","1:IV.C","1:IV.13"],"links":["1:IV.C","1:IV.13"],"implied":[{"id":"1:III.1","via":"1:III.2"},{"id":"1:III.2","via":"1:IV.C"}],"depth":19,"weight":164,"pos":[438.1,3289.1,25.2],"landmark":false,"img":{"s":[983,1572]}},{"id":"1:VI.5","label":"VI.5","course":"1","kind":"Lemma","chapter":"VI","name":null,"page":76,"title":"Stetigkeit koordinatenweise","note":null,"deps":["1:VI.3","1:IV.13"],"links":["1:VI.3","1:IV.13"],"implied":[],"depth":19,"weight":0,"pos":[1996.7,2944.3,6],"landmark":false,"img":{"s":[983,80],"p":[983,34]}},{"id":"1:VIII.2","label":"VIII.2","course":"1","kind":"Lemma","chapter":"VIII","name":null,"page":93,"title":"Ableitung koordinatenweise","note":"Kein eigener Beweis: folgt aus Satz IV.13","deps":["1:VIII.1","1:IV.13","1:VI.14"],"links":["1:VIII.1","1:IV.13","1:VI.14"],"implied":[],"depth":19,"weight":93,"pos":[2208.3,3298.1,20.5],"landmark":false,"img":{"s":[983,752]}},{"id":"2:VI.8","label":"VI.8","course":"2","kind":"Satz","chapter":"VI","name":"Vollständigkeit von C 0 (I, R n )","page":110,"title":"C⁰(I, ℝⁿ) ist ein Banachraum","note":null,"deps":["2:IV.4","1:IX.2","1:IX.3","1:III.24"],"links":["2:IV.4","1:IX.2","1:IX.3","1:III.24"],"implied":[],"depth":19,"weight":14,"pos":[4433.1,5741.1,11.6],"landmark":false,"img":{"s":[983,70],"p":[983,406]}},{"id":"1:VIII.18","label":"VIII.18","course":"1","kind":"Definition","chapter":"VIII","name":null,"page":103,"title":"Höhere Ableitungen","note":null,"deps":["1:VIII.3"],"links":["1:VIII.3"],"implied":[],"depth":19,"weight":56,"pos":[2332.5,3300.9,17.2],"landmark":false,"img":{"s":[983,347]}},{"id":"1:XI.1","label":"XI.1","course":"1","kind":"Definition","chapter":"XI","name":null,"page":127,"title":"Stammfunktion","note":null,"deps":["1:VIII.3"],"links":["1:VIII.3"],"implied":[],"depth":19,"weight":97,"pos":[3776.2,3434.2,20.8],"landmark":false,"img":{"s":[983,141]}},{"id":"2:VI.1","label":"VI.1","course":"2","kind":"Definition","chapter":"VI","name":null,"page":101,"title":"Gewöhnliche Differentialgleichung","note":null,"deps":["1:VIII.3"],"links":["1:VIII.3"],"implied":[],"depth":19,"weight":22,"pos":[4496.8,5414.8,13],"landmark":false,"img":{"s":[983,1421]}},{"id":"2:II.3","label":"II.3","course":"2","kind":"Definition","chapter":"II","name":"C k - Räume","page":15,"title":"Räume Cᵏ(Ω)","note":null,"deps":["2:II.1","2:I.17"],"links":["2:II.1","2:I.17"],"implied":[],"depth":19,"weight":93,"pos":[3333.4,5177.3,20.5],"landmark":false,"img":{"s":[983,594]}},{"id":"3:I.17","label":"I.17","course":"3","kind":"Satz","chapter":"I","name":null,"page":12,"title":"Summe, Produkt, Betrag messbarer Funktionen","note":null,"deps":["3:I.16","3:I.15"],"links":["3:I.16","3:I.15"],"implied":[],"depth":19,"weight":46,"pos":[3020.7,7700.5,16.2],"landmark":false,"img":{"s":[983,249],"p":[983,1995]}},{"id":"1:VIII.4","label":"VIII.4","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":95,"title":"Ableitung über lineare Approximation","note":null,"deps":["1:VIII.1","1:VI.15"],"links":["1:VIII.1","1:VI.15"],"implied":[],"depth":19,"weight":153,"pos":[2209.4,3221.1,24.6],"landmark":false,"img":{"s":[983,241],"p":[983,181]}},{"id":"1:VIII.7","label":"VIII.7","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":97,"title":"Kettenregel","note":null,"deps":["1:VIII.1","1:VI.11","1:VI.15"],"links":["1:VIII.1","1:VI.11","1:VI.15"],"implied":[],"depth":19,"weight":93,"pos":[2273.1,3264.5,20.5],"landmark":false,"img":{"s":[983,151],"p":[983,580]}},{"id":"1:VIII.12","label":"VIII.12","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":99,"title":"Lokales Extremum ⇒ f′ = 0","note":null,"deps":["1:VIII.11","1:VIII.1","1:VI.15"],"links":["1:VIII.11","1:VIII.1","1:VI.15"],"implied":[],"depth":19,"weight":131,"pos":[2141.5,3262.7,23.2],"landmark":false,"img":{"s":[983,76],"p":[983,640]}},{"id":"1:VII.7","label":"VII.7","course":"1","kind":"Satz","chapter":"VII","name":null,"page":83,"title":"Satz über die Umkehrfunktion","note":null,"deps":["1:VII.2","1:VII.6","1:VII.5","1:VI.1"],"links":["1:VII.2","1:VII.6"],"implied":[{"id":"1:VII.5","via":"1:VII.6"},{"id":"1:VI.1","via":"1:VII.2"}],"depth":19,"weight":21,"pos":[1270.2,3452.8,12.9],"landmark":true,"img":{"s":[983,325],"p":[983,1556]}},{"id":"2:III.31","label":"III.31","course":"2","kind":"Satz","chapter":"III","name":null,"page":50,"title":"Stetigkeit parameterabhängiger Integrale","note":null,"deps":["2:I.23","2:I.15","1:X.8"],"links":["2:I.23","1:X.8"],"implied":[{"id":"2:I.15","via":"2:I.23"}],"depth":19,"weight":15,"pos":[4007.1,5332.5,11.8],"landmark":false,"img":{"s":[983,201],"p":[983,427]}},{"id":"2:III.4","label":"III.4","course":"2","kind":"Lemma","chapter":"III","name":null,"page":30,"title":"Verbindung durch Polygonzüge","note":null,"deps":["2:III.3","2:I.21","2:I.23","2:I.8"],"links":["2:III.3","2:I.21","2:I.23","2:I.8"],"implied":[],"depth":19,"weight":3,"pos":[4094,5359.8,8.6],"landmark":false,"img":{"s":[983,99],"p":[983,964]}},{"id":"2:I.27","label":"I.27","course":"2","kind":"Lemma","chapter":"I","name":null,"page":11,"title":"Stetige Bilder zusammenhängender Räume","note":null,"deps":["2:I.25","2:I.20"],"links":["2:I.25","2:I.20"],"implied":[],"depth":19,"weight":1,"pos":[2493.4,5305.7,7.5],"landmark":false,"img":{"s":[983,174],"p":[983,202]}},{"id":"1:IV.27","label":"IV.27","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":53,"title":"Zerlegung nach Nullstellen","note":null,"deps":["1:IV.24","1:IV.26","1:II.3"],"links":["1:IV.26"],"implied":[{"id":"1:IV.24","via":"1:IV.26"},{"id":"1:II.3","via":"1:IV.26"}],"depth":19,"weight":4,"pos":[906.6,2668.2,9],"landmark":false,"img":{"s":[983,324],"p":[983,798]}},{"id":"L:18.17","label":"18.17","course":"L","kind":"Satz","chapter":"18","name":"Parallelogramm-Identität","page":196,"title":"Parallelogramm-Identität","note":null,"deps":["L:18.15"],"links":["L:18.15"],"implied":[],"depth":19,"weight":14,"pos":[7165,1936.9,11.6],"landmark":false,"img":{"s":[983,718],"p":[983,546]}},{"id":"L:18.27","label":"18.27","course":"L","kind":"Satz","chapter":"18","name":"Pythagoras","page":201,"title":"Satz des Pythagoras","note":null,"deps":["L:18.25","L:18.15"],"links":["L:18.25","L:18.15"],"implied":[],"depth":19,"weight":1,"pos":[7214.9,1925.9,7.5],"landmark":false,"img":{"s":[983,449],"p":[983,276]}},{"id":"L:19.17","label":"19.17","course":"L","kind":"Definition","chapter":"19","name":null,"page":227,"title":"Lineare Isometrie","note":null,"deps":["L:18.15","L:9.1"],"links":["L:18.15","L:9.1"],"implied":[],"depth":19,"weight":15,"pos":[7080.1,2409.1,11.8],"landmark":false,"img":{"s":[983,176]}},{"id":"L:18.31","label":"18.31","course":"L","kind":"Lemma","chapter":"18","name":null,"page":202,"title":"Rechnen mit Orthonormalbasen","note":null,"deps":["L:18.28","L:7.15"],"links":["L:18.28","L:7.15"],"implied":[],"depth":19,"weight":68,"pos":[7060.3,2032.8,18.4],"landmark":false,"img":{"s":[983,695],"p":[983,502]}},{"id":"L:10.2","label":"10.2","course":"L","kind":"Satz","chapter":"10","name":null,"page":126,"title":"Hom(V, W) ≅ K^{m×n}","note":null,"deps":["L:10.1","L:9.29"],"links":["L:10.1","L:9.29"],"implied":[],"depth":19,"weight":74,"pos":[5446.3,2633.2,18.9],"landmark":false,"img":{"s":[983,784]}},{"id":"L:14.5","label":"14.5","course":"L","kind":"Korollar","chapter":"14","name":null,"page":157,"title":"n verschiedene Eigenwerte ⇒ diagonalisierbar","note":null,"deps":["L:14.3","L:13.3"],"links":["L:14.3"],"implied":[{"id":"L:13.3","via":"L:14.3"}],"depth":19,"weight":0,"pos":[5492.7,2900.5,6],"landmark":false,"img":{"s":[983,155]}},{"id":"1:VII.4","label":"VII.4","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":82,"title":"f([a,b]) = [min, max]","note":"Kein eigener Beweis: Kombination von VII.2 und VII.3","deps":["1:VII.2","1:VII.3","1:IV.20"],"links":["1:VII.2","1:VII.3","1:IV.20"],"implied":[],"depth":20,"weight":8,"pos":[1292.9,3503.1,10.2],"landmark":false,"img":{"s":[983,169]}},{"id":"1:X.11","label":"X.11","course":"1","kind":"Satz","chapter":"X","name":null,"page":123,"title":"Stetige Funktionen sind integrierbar","note":null,"deps":["1:X.10","1:X.7","1:X.9","1:IV.20"],"links":["1:X.10","1:X.7","1:X.9","1:IV.20"],"implied":[],"depth":20,"weight":96,"pos":[3273.2,2883.2,20.7],"landmark":true,"img":{"s":[983,40],"p":[983,784]}},{"id":"2:I.16","label":"I.16","course":"2","kind":"Satz","chapter":"I","name":null,"page":8,"title":"Heine-Borel im ℝⁿ","note":"Kein eigener Beweis: Ana I, Satz IV.20","deps":["2:I.15","1:IV.20"],"links":["2:I.15","1:IV.20"],"implied":[],"depth":20,"weight":18,"pos":[2601.1,5151.9,12.4],"landmark":false,"img":{"s":[983,169]}},{"id":"1:V.2","label":"V.2","course":"1","kind":"Satz","chapter":"V","name":null,"page":57,"title":"Cauchy-Kriterium für Reihen","note":null,"deps":["1:V.1","1:III.23","1:III.24","1:III.10"],"links":["1:V.1","1:III.23","1:III.24"],"implied":[{"id":"1:III.10","via":"1:V.1"}],"depth":20,"weight":97,"pos":[474.4,3358.2,20.8],"landmark":false,"img":{"s":[983,293],"p":[983,399]}},{"id":"1:V.3","label":"V.3","course":"1","kind":"Satz","chapter":"V","name":"Leibniz-Kriterium","page":57,"title":"Leibniz-Kriterium","note":null,"deps":["1:V.1","1:III.10","1:III.7","1:III.8"],"links":["1:V.1"],"implied":[{"id":"1:III.10","via":"1:V.1"},{"id":"1:III.7","via":"1:V.1"},{"id":"1:III.8","via":"1:V.1"}],"depth":20,"weight":9,"pos":[531.9,3331.9,10.5],"landmark":false,"img":{"s":[983,347],"p":[983,1723]}},{"id":"1:V.4","label":"V.4","course":"1","kind":"Definition","chapter":"V","name":null,"page":59,"title":"Absolute Konvergenz","note":null,"deps":["1:V.1","1:IV.22"],"links":["1:V.1","1:IV.22"],"implied":[],"depth":20,"weight":91,"pos":[295,3404.5,20.3],"landmark":false,"img":{"s":[983,135]}},{"id":"1:V.9","label":"V.9","course":"1","kind":"Definition","chapter":"V","name":null,"page":64,"title":"Potenzreihe","note":null,"deps":["1:V.1"],"links":["1:V.1"],"implied":[],"depth":20,"weight":18,"pos":[416.5,3388.1,12.4],"landmark":false,"img":{"s":[983,209]}},{"id":"1:V.16","label":"V.16","course":"1","kind":"Lemma","chapter":"V","name":null,"page":68,"title":"Konjugation und Reihen","note":null,"deps":["1:V.1","1:IV.21","1:IV.22"],"links":["1:V.1","1:IV.22"],"implied":[{"id":"1:IV.21","via":"1:IV.22"}],"depth":20,"weight":34,"pos":[361.8,3410.5,14.7],"landmark":false,"img":{"s":[983,134],"p":[983,180]}},{"id":"3:I.5","label":"I.5","course":"3","kind":"Definition","chapter":"I","name":null,"page":5,"title":"Maß, Maßraum","note":null,"deps":["3:I.1","1:V.1"],"links":["3:I.1","1:V.1"],"implied":[],"depth":20,"weight":104,"pos":[3081.3,7383,21.3],"landmark":true,"img":{"s":[983,516]}},{"id":"3:II.1","label":"II.1","course":"3","kind":"Definition","chapter":"II","name":null,"page":17,"title":"Äußeres Maß","note":null,"deps":["1:VOR","1:V.1"],"links":["1:V.1"],"implied":[{"id":"1:VOR","via":"1:V.1"}],"depth":20,"weight":73,"pos":[4442.1,7402.1,18.8],"landmark":false,"img":{"s":[983,402]}},{"id":"1:VIII.19","label":"VIII.19","course":"1","kind":"Definition","chapter":"VIII","name":null,"page":103,"title":"Räume Cᵏ und C^∞","note":null,"deps":["1:VIII.18","1:VI.1"],"links":["1:VIII.18","1:VI.1"],"implied":[],"depth":20,"weight":53,"pos":[2163,3350.6,16.9],"landmark":false,"img":{"s":[983,1283]}},{"id":"2:VI.2","label":"VI.2","course":"2","kind":"Definition","chapter":"VI","name":null,"page":102,"title":"Lineare Differentialgleichung","note":null,"deps":["2:VI.1","L:9.1"],"links":["2:VI.1","L:9.1"],"implied":[],"depth":20,"weight":7,"pos":[4457.5,5530.8,10],"landmark":false,"img":{"s":[983,1595]}},{"id":"2:VI.13","label":"VI.13","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":114,"title":"Vergleichssatz (strikte Differentialungleichung)","note":null,"deps":["2:VI.1","1:VII.1","1:VIII.1"],"links":["2:VI.1","1:VII.1"],"implied":[{"id":"1:VIII.1","via":"2:VI.1"}],"depth":20,"weight":1,"pos":[4479.6,5486.5,7.5],"landmark":false,"img":{"s":[983,309],"p":[983,1335]}},{"id":"2:IV.1","label":"IV.1","course":"2","kind":"Definition","chapter":"IV","name":null,"page":59,"title":"Diffeomorphismus","note":null,"deps":["2:II.3","1:II.7"],"links":["2:II.3"],"implied":[{"id":"1:II.7","via":"2:II.3"}],"depth":20,"weight":31,"pos":[3133.8,5624.9,14.4],"landmark":false,"img":{"s":[983,1853]}},{"id":"2:IV.11","label":"IV.11","course":"2","kind":"Definition","chapter":"IV","name":"Untermannigfaltigkeit","page":71,"title":"Untermannigfaltigkeit","note":null,"deps":["2:II.3","L:8.1"],"links":["2:II.3","L:8.1"],"implied":[],"depth":20,"weight":21,"pos":[3020.2,5630.4,12.9],"landmark":false,"img":{"s":[983,383]}},{"id":"3:IX.4","label":"IX.4","course":"3","kind":"Definition","chapter":"IX","name":null,"page":109,"title":"Der Raum C¹(Ω̄)","note":null,"deps":["2:II.3","2:I.11"],"links":["2:II.3","2:I.11"],"implied":[],"depth":20,"weight":4,"pos":[3735.9,8139.3,9],"landmark":false,"img":{"s":[983,71]}},{"id":"1:VIII.5","label":"VIII.5","course":"1","kind":"Lemma","chapter":"VIII","name":null,"page":95,"title":"Differenzierbar ⇒ stetig","note":null,"deps":["1:VIII.4","1:VI.11","1:VI.15"],"links":["1:VIII.4","1:VI.11"],"implied":[{"id":"1:VI.15","via":"1:VIII.4"}],"depth":20,"weight":137,"pos":[2271.4,3340.5,23.6],"landmark":false,"img":{"s":[983,79],"p":[983,179]}},{"id":"2:II.7","label":"II.7","course":"2","kind":"Definition","chapter":"II","name":"Ableitung","page":19,"title":"(Totale) Ableitung","note":null,"deps":["2:I.4","1:VIII.4","1:VI.10","L:9.1","L:10.1"],"links":["2:I.4","1:VIII.4","L:10.1"],"implied":[{"id":"1:VI.10","via":"1:VIII.4"},{"id":"L:9.1","via":"L:10.1"}],"depth":20,"weight":101,"pos":[3332,5103.8,21.1],"landmark":true,"img":{"s":[983,683]}},{"id":"1:VII.8","label":"VII.8","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":84,"title":"Randpunkte unter der Umkehrfunktion","note":null,"deps":["1:VII.7"],"links":["1:VII.7"],"implied":[],"depth":20,"weight":4,"pos":[1249,3529.6,9],"landmark":false,"img":{"s":[983,74],"p":[983,635]}},{"id":"1:IV.29","label":"IV.29","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":54,"title":"Zerfall in Linearfaktoren über ℂ","note":null,"deps":["1:IV.27","1:IV.28"],"links":["1:IV.27","1:IV.28"],"implied":[],"depth":20,"weight":3,"pos":[737.1,2758.6,8.6],"landmark":false,"img":{"s":[983,249],"p":[983,289]}},{"id":"L:19.20","label":"19.20","course":"L","kind":"Satz","chapter":"19","name":null,"page":229,"title":"Isometrie ⇔ erhält das Skalarprodukt","note":null,"deps":["L:19.17","L:18.17"],"links":["L:19.17","L:18.17"],"implied":[],"depth":20,"weight":13,"pos":[7149.6,2477.6,11.4],"landmark":false,"img":{"s":[983,193],"p":[983,690]}},{"id":"L:18.33","label":"18.33","course":"L","kind":"Satz","chapter":"18","name":"Orthogonalisierungs-Verfahren von Gram–Schmidt","page":203,"title":"Gram-Schmidt-Verfahren","note":null,"deps":["L:18.28","L:18.31","L:7.5"],"links":["L:18.31","L:7.5"],"implied":[{"id":"L:18.28","via":"L:18.31"}],"depth":20,"weight":55,"pos":[7015.4,2083.2,17.1],"landmark":true,"img":{"s":[983,520],"p":[983,1677]}},{"id":"L:18.49","label":"18.49","course":"L","kind":"Lemma","chapter":"18","name":null,"page":213,"title":"Basiswechsel zwischen Orthonormalbasen","note":null,"deps":["L:18.48","L:18.31","L:7.19"],"links":["L:18.48","L:18.31","L:7.19"],"implied":[],"depth":20,"weight":37,"pos":[7120.5,2133.7,15.1],"landmark":false,"img":{"s":[983,237]}},{"id":"L:10.4","label":"10.4","course":"L","kind":"Satz","chapter":"10","name":null,"page":127,"title":"Isomorphismus ⇔ invertierbare Matrix","note":null,"deps":["L:10.3","L:10.2","L:5.55"],"links":["L:10.3","L:10.2","L:5.55"],"implied":[],"depth":20,"weight":73,"pos":[5492.1,2685.8,18.8],"landmark":true,"img":{"s":[983,199],"p":[983,1346]}},{"id":"1:X.13","label":"X.13","course":"1","kind":"Satz","chapter":"X","name":"Mittelwertsatz der Integralrechnung","page":124,"title":"Mittelwertsatz der Integralrechnung","note":null,"deps":["1:X.12","1:X.4","1:VII.4","1:VII.1","1:VI.6"],"links":["1:X.12","1:X.4","1:VII.4","1:VI.6"],"implied":[{"id":"1:VII.1","via":"1:VII.4"}],"depth":21,"weight":7,"pos":[3196.1,2933.7,10],"landmark":false,"img":{"s":[983,214],"p":[983,1637]}},{"id":"1:XI.3","label":"XI.3","course":"1","kind":"Satz","chapter":"XI","name":"Hauptsatz der Differential- und Integralrechnung","page":128,"title":"Hauptsatz der Differential- und Integralrechnung","note":null,"deps":["1:X.11","1:X.6","1:X.8","1:VI.1","1:XI.1","1:VIII.1"],"links":["1:X.11","1:XI.1"],"implied":[{"id":"1:X.6","via":"1:X.11"},{"id":"1:X.8","via":"1:X.11"},{"id":"1:VI.1","via":"1:X.11"},{"id":"1:VIII.1","via":"1:XI.1"}],"depth":21,"weight":95,"pos":[3702.6,3515.4,20.6],"landmark":true,"img":{"s":[983,318],"p":[983,356]}},{"id":"1:V.7","label":"V.7","course":"1","kind":"Satz","chapter":"V","name":"Quotientenkriterium","page":60,"title":"Quotientenkriterium","note":null,"deps":["1:V.2","1:V.1","1:III.19","1:II.5"],"links":["1:V.2","1:II.5"],"implied":[{"id":"1:V.1","via":"1:V.2"},{"id":"1:III.19","via":"1:V.2"}],"depth":21,"weight":38,"pos":[520.2,3408.4,15.2],"landmark":true,"img":{"s":[983,218],"p":[983,3052]}},{"id":"1:V.8","label":"V.8","course":"1","kind":"Satz","chapter":"V","name":"Wurzelkriterium","page":62,"title":"Wurzelkriterium","note":null,"deps":["1:V.2","1:III.19","1:III.15","1:II.5"],"links":["1:V.2","1:II.5"],"implied":[{"id":"1:III.19","via":"1:V.2"},{"id":"1:III.15","via":"1:V.2"}],"depth":21,"weight":13,"pos":[463,3421.4,11.4],"landmark":false,"img":{"s":[983,277],"p":[983,2024]}},{"id":"1:XI.10","label":"XI.10","course":"1","kind":"Satz","chapter":"XI","name":"Integralvergleichskriterium für Reihen","page":135,"title":"Integralvergleichskriterium für Reihen","note":null,"deps":["1:XI.8","1:X.12","1:X.6","1:V.2","1:VII.6"],"links":["1:XI.8","1:X.12","1:X.6","1:V.2","1:VII.6"],"implied":[],"depth":21,"weight":0,"pos":[3618.8,3524.6,6],"landmark":false,"img":{"s":[983,115],"p":[983,1740]}},{"id":"1:V.5","label":"V.5","course":"1","kind":"Satz","chapter":"V","name":null,"page":59,"title":"Absolut konvergent ⇒ konvergent","note":null,"deps":["1:V.4","1:V.2","1:IV.8"],"links":["1:V.4","1:V.2"],"implied":[{"id":"1:IV.8","via":"1:V.4"}],"depth":21,"weight":66,"pos":[337.3,3471.6,18.2],"landmark":false,"img":{"s":[983,140],"p":[983,373]}},{"id":"1:V.15","label":"V.15","course":"1","kind":"Satz","chapter":"V","name":"Cauchy-Produkt","page":67,"title":"Cauchy-Produkt","note":null,"deps":["1:V.4","1:V.2"],"links":["1:V.4","1:V.2"],"implied":[],"depth":21,"weight":34,"pos":[274.7,3489,14.7],"landmark":true,"img":{"s":[983,265],"p":[983,1239]}},{"id":"1:V.11","label":"V.11","course":"1","kind":"Lemma","chapter":"V","name":null,"page":64,"title":"Abschätzung des Potenzreihen-Rests","note":null,"deps":["1:V.9","1:V.4","1:V.2","1:III.6","1:II.5"],"links":["1:V.9","1:V.4","1:V.2","1:II.5"],"implied":[{"id":"1:III.6","via":"1:V.9"}],"depth":21,"weight":13,"pos":[498.7,3463,11.4],"landmark":false,"img":{"s":[983,442],"p":[983,486]}},{"id":"1:IX.8","label":"IX.8","course":"1","kind":"Satz","chapter":"IX","name":"Abelscher Grenzwertsatz","page":116,"title":"Abelscher Grenzwertsatz","note":null,"deps":["1:V.1","1:V.9","1:II.5","1:III.2"],"links":["1:V.9","1:II.5"],"implied":[{"id":"1:V.1","via":"1:V.9"},{"id":"1:III.2","via":"1:V.1"}],"depth":21,"weight":0,"pos":[2832.5,3252.3,6],"landmark":false,"img":{"s":[983,270],"p":[983,1266]}},{"id":"2:III.26","label":"III.26","course":"2","kind":"Definition","chapter":"III","name":null,"page":44,"title":"Analytische Funktion","note":null,"deps":["1:V.9"],"links":["1:V.9"],"implied":[],"depth":21,"weight":1,"pos":[4192.2,4965.9,7.5],"landmark":false,"img":{"s":[983,281]}},{"id":"3:I.6","label":"I.6","course":"3","kind":"Definition","chapter":"I","name":null,"page":5,"title":"Endliche und σ-endliche Maße","note":null,"deps":["3:I.5"],"links":["3:I.5"],"implied":[],"depth":21,"weight":46,"pos":[3103.3,7448.9,16.2],"landmark":false,"img":{"s":[983,1008]}},{"id":"3:I.7","label":"I.7","course":"3","kind":"Satz","chapter":"I","name":"Stetigkeits-Eigenschaften von Maßen","page":6,"title":"Stetigkeit von Maßen","note":null,"deps":["3:I.5","1:III.10"],"links":["3:I.5"],"implied":[{"id":"1:III.10","via":"3:I.5"}],"depth":21,"weight":72,"pos":[3194.2,7516.6,18.7],"landmark":false,"img":{"s":[983,989],"p":[983,790]}},{"id":"3:I.8","label":"I.8","course":"3","kind":"Definition","chapter":"I","name":null,"page":7,"title":"Nullmenge, vollständiges Maß","note":null,"deps":["3:I.5"],"links":["3:I.5"],"implied":[],"depth":21,"weight":88,"pos":[3035.6,7440.4,20.1],"landmark":false,"img":{"s":[983,928]}},{"id":"3:II.11","label":"II.11","course":"3","kind":"Definition","chapter":"II","name":null,"page":22,"title":"Prämaß","note":null,"deps":["3:II.10","3:I.5"],"links":["3:II.10","3:I.5"],"implied":[],"depth":21,"weight":55,"pos":[4421.7,7516.8,17.1],"landmark":false,"img":{"s":[983,868]}},{"id":"3:VI.1","label":"VI.1","course":"3","kind":"Definition","chapter":"VI","name":null,"page":76,"title":"Produktmaß","note":null,"deps":["3:II.1"],"links":["3:II.1"],"implied":[],"depth":21,"weight":19,"pos":[3376.4,8014.8,12.5],"landmark":false,"img":{"s":[983,163]}},{"id":"2:III.21","label":"III.21","course":"2","kind":"Lemma","chapter":"III","name":null,"page":41,"title":"Taylorpolynom","note":null,"deps":["1:VIII.19","1:IV.23"],"links":["1:VIII.19","1:IV.23"],"implied":[],"depth":21,"weight":10,"pos":[4129.6,4976.2,10.7],"landmark":false,"img":{"s":[983,211],"p":[983,477]}},{"id":"2:V.1","label":"V.1","course":"2","kind":"Definition","chapter":"V","name":null,"page":77,"title":"Parametrisierte Kurve","note":null,"deps":["1:VIII.19"],"links":["1:VIII.19"],"implied":[],"depth":21,"weight":28,"pos":[5012.3,5074.6,13.9],"landmark":false,"img":{"s":[983,504]}},{"id":"3:IX.6","label":"IX.6","course":"3","kind":"Lemma","chapter":"IX","name":null,"page":110,"title":"Zerlegung der Eins","note":null,"deps":["3:V.16","2:I.21","1:VIII.19"],"links":["3:V.16","2:I.21","1:VIII.19"],"implied":[],"depth":21,"weight":3,"pos":[3799.3,8194,8.6],"landmark":false,"img":{"s":[983,183],"p":[983,714]}},{"id":"2:VI.4","label":"VI.4","course":"2","kind":"Satz","chapter":"VI","name":null,"page":106,"title":"Inhomogen = homogen + spezielle Lösung","note":null,"deps":["2:VI.2","L:11.6"],"links":["2:VI.2","L:11.6"],"implied":[],"depth":21,"weight":0,"pos":[4484.6,5570.4,6],"landmark":false,"img":{"s":[983,771]}},{"id":"3:VII.1","label":"VII.1","course":"3","kind":"Definition","chapter":"VII","name":null,"page":88,"title":"C¹-Diffeomorphismus","note":null,"deps":["2:IV.1"],"links":["2:IV.1"],"implied":[],"depth":21,"weight":14,"pos":[4132.6,8082.6,11.6],"landmark":false,"img":{"s":[983,529]}},{"id":"3:VIII.4","label":"VIII.4","course":"3","kind":"Definition","chapter":"VIII","name":"Untermannigfaltigkeit","page":99,"title":"Untermannigfaltigkeit (Plättung)","note":null,"deps":["2:IV.11","2:IV.1"],"links":["2:IV.11","2:IV.1"],"implied":[],"depth":21,"weight":15,"pos":[4980.9,8033.5,11.8],"landmark":false,"img":{"s":[983,414]}},{"id":"1:VIII.6","label":"VIII.6","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":95,"title":"Summen-, Produkt-, Quotientenregel","note":null,"deps":["1:VIII.1","1:VIII.5","1:VI.15","1:VI.6"],"links":["1:VIII.5","1:VI.6"],"implied":[{"id":"1:VIII.1","via":"1:VIII.5"},{"id":"1:VI.15","via":"1:VIII.5"}],"depth":21,"weight":136,"pos":[2217.5,3398.3,23.5],"landmark":false,"img":{"s":[983,320],"p":[983,1712]}},{"id":"2:II.10","label":"II.10","course":"2","kind":"Satz","chapter":"II","name":null,"page":23,"title":"Differenzierbar ⇒ stetig","note":null,"deps":["2:II.7"],"links":["2:II.7"],"implied":[],"depth":21,"weight":1,"pos":[3298.8,5226.3,7.5],"landmark":false,"img":{"s":[983,69],"p":[983,344]}},{"id":"2:II.11","label":"II.11","course":"2","kind":"Satz","chapter":"II","name":"Kettenregel","page":23,"title":"Kettenregel","note":null,"deps":["2:II.7","1:IV.11"],"links":["2:II.7","1:IV.11"],"implied":[],"depth":21,"weight":76,"pos":[3360.4,5243.5,19.1],"landmark":true,"img":{"s":[983,288],"p":[983,1227]}},{"id":"2:II.12","label":"II.12","course":"2","kind":"Satz","chapter":"II","name":null,"page":24,"title":"Ableitung komponentenweise","note":null,"deps":["2:II.7"],"links":["2:II.7"],"implied":[],"depth":21,"weight":71,"pos":[3262.4,5181,18.6],"landmark":false,"img":{"s":[983,127],"p":[983,382]}},{"id":"2:III.11","label":"III.11","course":"2","kind":"Definition","chapter":"III","name":null,"page":33,"title":"Kritischer Punkt","note":null,"deps":["2:II.7"],"links":["2:II.7"],"implied":[],"depth":21,"weight":0,"pos":[4125.4,5229.5,6],"landmark":false,"img":{"s":[983,335]}},{"id":"2:IV.13","label":"IV.13","course":"2","kind":"Definition","chapter":"IV","name":null,"page":73,"title":"Tangentialraum","note":null,"deps":["2:IV.11","2:II.7"],"links":["2:IV.11","2:II.7"],"implied":[],"depth":21,"weight":7,"pos":[3045.9,5698.2,10],"landmark":false,"img":{"s":[983,183]}},{"id":"2:V.25","label":"V.25","course":"2","kind":"Definition","chapter":"V","name":null,"page":92,"title":"Geschlossene und exakte 1-Formen","note":null,"deps":["2:V.23","2:II.7"],"links":["2:V.23","2:II.7"],"implied":[],"depth":21,"weight":0,"pos":[4904.9,5325.6,6],"landmark":false,"img":{"s":[983,1225]}},{"id":"2:VI.5","label":"VI.5","course":"2","kind":"Definition","chapter":"VI","name":null,"page":106,"title":"Erstes Integral","note":null,"deps":["2:VI.1","2:II.7"],"links":["2:VI.1","2:II.7"],"implied":[],"depth":21,"weight":0,"pos":[4427.8,5664.3,6],"landmark":false,"img":{"s":[983,2552]}},{"id":"3:VIII.1","label":"VIII.1","course":"3","kind":"Definition","chapter":"VIII","name":null,"page":97,"title":"Immersion, Gramsche Matrix","note":null,"deps":["2:II.7","L:9.21","L:18.7"],"links":["2:II.7","L:9.21","L:18.7"],"implied":[],"depth":21,"weight":13,"pos":[5034.8,8045.9,11.4],"landmark":false,"img":{"s":[983,533]}},{"id":"1:VIII.8","label":"VIII.8","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":97,"title":"Ableitung der Umkehrfunktion","note":null,"deps":["1:VII.7","1:VII.8","1:VIII.1","1:VI.15"],"links":["1:VII.8","1:VIII.1","1:VI.15"],"implied":[{"id":"1:VII.7","via":"1:VII.8"}],"depth":21,"weight":3,"pos":[2281.4,3403.9,8.6],"landmark":false,"img":{"s":[983,211],"p":[983,1113]}},{"id":"1:IV.30","label":"IV.30","course":"1","kind":"Lemma","chapter":"IV","name":null,"page":54,"title":"Reelle Polynome: konjugierte Nullstellen","note":null,"deps":["1:IV.29","1:IV.24","1:IV.26","1:IV.21","1:IV.22"],"links":["1:IV.29","1:IV.22"],"implied":[{"id":"1:IV.24","via":"1:IV.29"},{"id":"1:IV.26","via":"1:IV.29"},{"id":"1:IV.21","via":"1:IV.22"}],"depth":21,"weight":1,"pos":[732.9,2814.4,7.5],"landmark":false,"img":{"s":[983,304],"p":[983,915]}},{"id":"L:21.35","label":"21.35","course":"L","kind":"Satz","chapter":"21","name":"Struktur von euklidischen Isometrien","page":273,"title":"Bewegung = Translation ∘ lineare Isometrie","note":null,"deps":["L:21.31","L:19.20"],"links":["L:21.31","L:19.20"],"implied":[],"depth":21,"weight":4,"pos":[7138.3,1982.2,9],"landmark":true,"img":{"s":[983,224]}},{"id":"L:18.36","label":"18.36","course":"L","kind":"Satz","chapter":"18","name":null,"page":206,"title":"Eigenschaften des Orthogonalkomplements","note":null,"deps":["L:18.35","L:18.33","L:8.10","L:8.2"],"links":["L:18.35","L:18.33","L:8.10"],"implied":[{"id":"L:8.2","via":"L:8.10"}],"depth":21,"weight":42,"pos":[6995.6,2146,15.7],"landmark":false,"img":{"s":[983,253],"p":[983,499]}},{"id":"L:18.46","label":"18.46","course":"L","kind":"Satz","chapter":"18","name":"Satz von Riesz","page":211,"title":"Satz von Riesz (Darstellung von Funktionalen)","note":null,"deps":["L:18.33","L:9.6"],"links":["L:18.33","L:9.6"],"implied":[],"depth":21,"weight":46,"pos":[7059.4,2150,16.2],"landmark":false,"img":{"s":[983,135],"p":[983,548]}},{"id":"2:III.15","label":"III.15","course":"2","kind":"Satz","chapter":"III","name":null,"page":35,"title":"Minimum einer quadratischen Form auf der Sphäre","note":null,"deps":["2:I.22","2:I.16","L:18.33","L:20.1"],"links":["2:I.22","2:I.16","L:18.33","L:20.1"],"implied":[],"depth":21,"weight":17,"pos":[4061.3,5318.4,12.2],"landmark":false,"img":{"s":[983,345],"p":[983,577]}},{"id":"L:18.50","label":"18.50","course":"L","kind":"Satz","chapter":"18","name":"Charakterisierung von orthogonalen Matrizen","page":213,"title":"Charakterisierung orthogonaler Matrizen","note":null,"deps":["L:18.48","L:18.49"],"links":["L:18.49"],"implied":[{"id":"L:18.48","via":"L:18.49"}],"depth":21,"weight":28,"pos":[7124.3,2201.1,13.9],"landmark":false,"img":{"s":[983,410]}},{"id":"L:18.51","label":"18.51","course":"L","kind":"Satz","chapter":"18","name":"Charakterisierung von unitären Matrizen","page":213,"title":"Charakterisierung unitärer Matrizen","note":null,"deps":["L:18.48","L:18.49"],"links":["L:18.49"],"implied":[{"id":"L:18.48","via":"L:18.49"}],"depth":21,"weight":6,"pos":[7190.9,2208.7,9.7],"landmark":false,"img":{"s":[983,282],"p":[983,288]}},{"id":"L:12.17","label":"12.17","course":"L","kind":"Satz","chapter":"12","name":null,"page":147,"title":"A invertierbar ⇔ det A ≠ 0","note":null,"deps":["L:12.16","L:12.8","L:10.4","L:8.22"],"links":["L:12.16","L:12.8","L:10.4","L:8.22"],"implied":[],"depth":21,"weight":71,"pos":[6246.3,2533.4,18.6],"landmark":true,"img":{"s":[983,36],"p":[983,233]}},{"id":"2:III.32","label":"III.32","course":"2","kind":"Satz","chapter":"III","name":null,"page":50,"title":"Differentiation unter dem Integral","note":null,"deps":["2:III.31","1:XI.3","2:I.23"],"links":["2:III.31","1:XI.3"],"implied":[{"id":"2:I.23","via":"2:III.31"}],"depth":22,"weight":14,"pos":[4155.8,5428.9,11.6],"landmark":false,"img":{"s":[983,518],"p":[983,2532]}},{"id":"2:VI.9","label":"VI.9","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":110,"title":"Anfangswertproblem als Integralgleichung","note":null,"deps":["2:VI.1","1:XI.3"],"links":["2:VI.1","1:XI.3"],"implied":[],"depth":22,"weight":14,"pos":[4511,5526.8,11.6],"landmark":false,"img":{"s":[983,509],"p":[983,150]}},{"id":"1:V.exp","label":"V.exp","course":"1","kind":"Definition","chapter":"V","name":null,"page":62,"title":"Exponentialfunktion exp(z)","note":"Im Skript als Beispiel nach Satz V.7 eingeführt","deps":["1:V.7","1:V.1"],"links":["1:V.7"],"implied":[{"id":"1:V.1","via":"1:V.7"}],"depth":22,"weight":37,"pos":[395,3554.2,15.1],"landmark":false,"img":{"s":[983,112]}},{"id":"1:V.10","label":"V.10","course":"1","kind":"Satz","chapter":"V","name":null,"page":64,"title":"Konvergenzradius","note":null,"deps":["1:V.8","1:V.9"],"links":["1:V.8","1:V.9"],"implied":[],"depth":22,"weight":12,"pos":[452.1,3542.1,11.2],"landmark":false,"img":{"s":[983,323]}},{"id":"1:V.6","label":"V.6","course":"1","kind":"Satz","chapter":"V","name":"Umordnungssatz","page":59,"title":"Umordnungssatz","note":null,"deps":["1:V.4","1:V.5","1:V.2","1:IV.8"],"links":["1:V.5"],"implied":[{"id":"1:V.4","via":"1:V.5"},{"id":"1:V.2","via":"1:V.5"},{"id":"1:IV.8","via":"1:V.4"}],"depth":22,"weight":49,"pos":[331.5,3538,16.5],"landmark":false,"img":{"s":[983,145],"p":[983,902]}},{"id":"1:V.12","label":"V.12","course":"1","kind":"Satz","chapter":"V","name":null,"page":65,"title":"Nullstellen häufen sich in 0 ⇒ Reihe = 0","note":null,"deps":["1:V.11","1:IV.15","1:II.3"],"links":["1:V.11","1:IV.15"],"implied":[{"id":"1:II.3","via":"1:V.11"}],"depth":22,"weight":1,"pos":[423,3479.2,7.5],"landmark":false,"img":{"s":[983,119],"p":[983,439]}},{"id":"3:II.2","label":"II.2","course":"3","kind":"Definition","chapter":"II","name":null,"page":17,"title":"Carathéodory-messbare Mengen","note":null,"deps":["3:II.1","3:I.7"],"links":["3:II.1","3:I.7"],"implied":[],"depth":22,"weight":66,"pos":[4411.6,7630.3,18.2],"landmark":false,"img":{"s":[983,712]}},{"id":"3:I.9","label":"I.9","course":"3","kind":"Satz","chapter":"I","name":null,"page":8,"title":"Vervollständigung eines Maßraums","note":null,"deps":["3:I.8","3:I.1"],"links":["3:I.8"],"implied":[{"id":"3:I.1","via":"3:I.8"}],"depth":22,"weight":44,"pos":[3058.4,7504.5,15.9],"landmark":false,"img":{"s":[983,76],"p":[983,451]}},{"id":"3:I.18","label":"I.18","course":"3","kind":"Definition","chapter":"I","name":null,"page":14,"title":"µ-messbare Funktion","note":null,"deps":["3:I.13","3:I.8"],"links":["3:I.13","3:I.8"],"implied":[],"depth":22,"weight":62,"pos":[3123.8,7511.6,17.8],"landmark":false,"img":{"s":[983,622]}},{"id":"3:II.12","label":"II.12","course":"3","kind":"Definition","chapter":"II","name":null,"page":23,"title":"Fortsetzung eines Prämaßes","note":null,"deps":["3:II.11","3:II.1"],"links":["3:II.11","3:II.1"],"implied":[],"depth":22,"weight":47,"pos":[4345.8,7620.9,16.3],"landmark":false,"img":{"s":[983,155]}},{"id":"3:II.26","label":"II.26","course":"3","kind":"Definition","chapter":"II","name":null,"page":29,"title":"Inhalt","note":null,"deps":["3:II.19","3:II.11"],"links":["3:II.19","3:II.11"],"implied":[],"depth":22,"weight":47,"pos":[4509.7,7587.4,16.3],"landmark":false,"img":{"s":[983,671]}},{"id":"3:VI.2","label":"VI.2","course":"3","kind":"Lemma","chapter":"VI","name":null,"page":76,"title":"Das Produktmaß ist ein äußeres Maß","note":null,"deps":["3:VI.1","3:II.1"],"links":["3:VI.1"],"implied":[{"id":"3:II.1","via":"3:VI.1"}],"depth":22,"weight":18,"pos":[3377.4,8077.2,12.4],"landmark":false,"img":{"s":[983,62],"p":[983,438]}},{"id":"2:III.25","label":"III.25","course":"2","kind":"Definition","chapter":"III","name":null,"page":44,"title":"Taylorreihe","note":null,"deps":["2:III.21","1:V.9"],"links":["2:III.21","1:V.9"],"implied":[],"depth":22,"weight":1,"pos":[4130.3,5057.4,7.5],"landmark":false,"img":{"s":[983,676]}},{"id":"2:V.2","label":"V.2","course":"2","kind":"Definition","chapter":"V","name":"Bogenlänge","page":77,"title":"Bogenlänge","note":null,"deps":["2:V.1","1:X.3","1:IV.7"],"links":["2:V.1","1:X.3"],"implied":[{"id":"1:IV.7","via":"2:V.1"}],"depth":22,"weight":25,"pos":[5014.8,5134,13.5],"landmark":false,"img":{"s":[983,1080]}},{"id":"2:V.3","label":"V.3","course":"2","kind":"Definition","chapter":"V","name":"Umparametrisierung","page":78,"title":"Umparametrisierung","note":null,"deps":["2:V.1","1:II.7"],"links":["2:V.1"],"implied":[{"id":"1:II.7","via":"2:V.1"}],"depth":22,"weight":5,"pos":[5069.3,5139.7,9.4],"landmark":false,"img":{"s":[983,344]}},{"id":"2:V.13","label":"V.13","course":"2","kind":"Definition","chapter":"V","name":null,"page":83,"title":"Geschlossene Kurve","note":null,"deps":["2:V.1"],"links":["2:V.1"],"implied":[],"depth":22,"weight":3,"pos":[4961.2,5141.4,8.6],"landmark":false,"img":{"s":[983,282]}},{"id":"1:VIII.13","label":"VIII.13","course":"1","kind":"Satz","chapter":"VIII","name":"Mittelwertsatz der Differentialrechnung","page":100,"title":"Mittelwertsatz (Satz von Rolle)","note":null,"deps":["1:VII.3","1:IV.20","1:VIII.12","1:VIII.6"],"links":["1:VII.3","1:IV.20","1:VIII.12","1:VIII.6"],"implied":[],"depth":22,"weight":129,"pos":[2153.4,3443.6,23],"landmark":true,"img":{"s":[983,165],"p":[983,464]}},{"id":"2:II.2","label":"II.2","course":"2","kind":"Satz","chapter":"II","name":"Ableitungsregeln","page":13,"title":"Rechenregeln für partielle Ableitungen","note":null,"deps":["2:II.1","1:VIII.6","1:VIII.7","1:VIII.2"],"links":["2:II.1","1:VIII.6","1:VIII.7","1:VIII.2"],"implied":[],"depth":22,"weight":85,"pos":[3403.8,5161,19.8],"landmark":false,"img":{"s":[983,2816]}},{"id":"2:II.13","label":"II.13","course":"2","kind":"Satz","chapter":"II","name":null,"page":24,"title":"Summen-, Produkt-, Quotientenregel","note":null,"deps":["2:II.7","2:II.10","1:IV.11"],"links":["2:II.10","1:IV.11"],"implied":[{"id":"2:II.7","via":"2:II.10"}],"depth":22,"weight":0,"pos":[3411.7,5218.3,6],"landmark":false,"img":{"s":[983,623],"p":[983,1439]}},{"id":"2:IV.2","label":"IV.2","course":"2","kind":"Lemma","chapter":"IV","name":null,"page":60,"title":"Ableitung der Umkehrabbildung","note":null,"deps":["2:IV.1","2:II.11","L:10.4"],"links":["2:IV.1","2:II.11","L:10.4"],"implied":[],"depth":22,"weight":26,"pos":[3101,5705.9,13.6],"landmark":false,"img":{"s":[983,178],"p":[983,765]}},{"id":"3:VIII.7","label":"VIII.7","course":"3","kind":"Definition","chapter":"VIII","name":null,"page":101,"title":"Lokale Parametrisierung","note":null,"deps":["3:VIII.4","3:VIII.1"],"links":["3:VIII.4","3:VIII.1"],"implied":[],"depth":22,"weight":10,"pos":[4961.4,8103.9,10.7],"landmark":false,"img":{"s":[983,99]}},{"id":"1:IV.31","label":"IV.31","course":"1","kind":"Satz","chapter":"IV","name":null,"page":55,"title":"Reelle Faktorisierung","note":"Kein eigener Beweis: folgt aus Lemma IV.30","deps":["1:IV.30"],"links":["1:IV.30"],"implied":[],"depth":22,"weight":0,"pos":[739.8,2874.7,6],"landmark":false,"img":{"s":[983,275]}},{"id":"L:21.36","label":"21.36","course":"L","kind":"Lemma","chapter":"21","name":null,"page":273,"title":"Isometrie durch affine Basis bestimmt","note":null,"deps":["L:21.35","L:21.16"],"links":["L:21.35","L:21.16"],"implied":[],"depth":22,"weight":0,"pos":[7180.8,2026.1,6],"landmark":false,"img":{"s":[983,76],"p":[983,1806]}},{"id":"L:18.39","label":"18.39","course":"L","kind":"Definition","chapter":"18","name":null,"page":207,"title":"Orthogonalprojektion","note":null,"deps":["L:18.36"],"links":["L:18.36"],"implied":[],"depth":22,"weight":2,"pos":[7165.4,2165.9,8.1],"landmark":false,"img":{"s":[983,504]}},{"id":"L:19.26","label":"19.26","course":"L","kind":"Satz","chapter":"19","name":null,"page":233,"title":"Isometrien sind Produkte von Spiegelungen","note":null,"deps":["L:19.17","L:18.36","1:II.3"],"links":["L:19.17","L:18.36","1:II.3"],"implied":[],"depth":22,"weight":0,"pos":[7190.8,2694.3,6],"landmark":false,"img":{"s":[983,125],"p":[983,769]}},{"id":"L:18.47","label":"18.47","course":"L","kind":"Korollar","chapter":"18","name":null,"page":212,"title":"V* ≅ V im euklidischen Fall","note":null,"deps":["L:18.46","L:9.23"],"links":["L:18.46","L:9.23"],"implied":[],"depth":22,"weight":0,"pos":[7072.8,2253,6],"landmark":false,"img":{"s":[983,227],"p":[983,1000]}},{"id":"L:19.2","label":"19.2","course":"L","kind":"Satz","chapter":"19","name":"Existenz und Matrixform von Φ ∗ ","page":218,"title":"Existenz und Matrix der Adjungierten","note":null,"deps":["L:19.1","L:18.46","L:18.31"],"links":["L:19.1","L:18.46"],"implied":[{"id":"L:18.31","via":"L:18.46"}],"depth":22,"weight":42,"pos":[7139.1,2679.8,15.7],"landmark":false,"img":{"s":[983,381],"p":[983,1538]}},{"id":"L:20.9","label":"20.9","course":"L","kind":"Satz","chapter":"20","name":null,"page":246,"title":"Bilinearformen als ⟨v, Φw⟩","note":null,"deps":["L:20.1","L:18.46"],"links":["L:20.1","L:18.46"],"implied":[],"depth":22,"weight":17,"pos":[6898.5,2872.1,12.2],"landmark":false,"img":{"s":[983,214],"p":[983,1292]}},{"id":"2:III.18","label":"III.18","course":"2","kind":"Satz","chapter":"III","name":"Hauptachsentransformation","page":37,"title":"Hauptachsentransformation","note":null,"deps":["2:III.15","1:II.3","L:18.33","L:18.36"],"links":["2:III.15","L:18.36"],"implied":[{"id":"1:II.3","via":"2:III.15"},{"id":"L:18.33","via":"2:III.15"}],"depth":22,"weight":13,"pos":[4103.8,5410.9,11.4],"landmark":false,"img":{"s":[983,150],"p":[983,2729]}},{"id":"L:18.54","label":"18.54","course":"L","kind":"Satz","chapter":"18","name":"Matrizen-Gruppen","page":214,"title":"Orthogonale und unitäre Gruppe","note":null,"deps":["L:18.50","L:5.56","L:5.25"],"links":["L:18.50","L:5.56","L:5.25"],"implied":[],"depth":22,"weight":20,"pos":[6979.9,2223.4,12.7],"landmark":false,"img":{"s":[983,281],"p":[983,262]}},{"id":"L:18.52","label":"18.52","course":"L","kind":"Korollar","chapter":"18","name":null,"page":214,"title":"Determinante orthogonaler/unitärer Matrizen","note":null,"deps":["L:18.50","L:18.51","L:12.16","L:12.14"],"links":["L:18.50","L:18.51","L:12.16","L:12.14"],"implied":[],"depth":22,"weight":5,"pos":[7119.7,2259.4,9.4],"landmark":false,"img":{"s":[983,87],"p":[983,254]}},{"id":"L:12.18","label":"12.18","course":"L","kind":"Korollar","chapter":"12","name":null,"page":147,"title":"det A⁻¹ und ähnliche Matrizen","note":null,"deps":["L:12.17","L:12.16","L:10.9"],"links":["L:12.17","L:10.9"],"implied":[{"id":"L:12.16","via":"L:12.17"}],"depth":22,"weight":1,"pos":[6318.6,2616.1,7.5],"landmark":false,"img":{"s":[983,303],"p":[983,217]}},{"id":"L:12.20","label":"12.20","course":"L","kind":"Satz","chapter":"12","name":"Determinante und Inverse einer Matrix","page":147,"title":"Inverse über die Adjunkte","note":null,"deps":["L:12.11","L:12.17"],"links":["L:12.17"],"implied":[{"id":"L:12.11","via":"L:12.17"}],"depth":22,"weight":26,"pos":[6270.9,2592.8,13.6],"landmark":false,"img":{"s":[983,154],"p":[983,582]}},{"id":"L:12.21","label":"12.21","course":"L","kind":"Satz","chapter":"12","name":null,"page":148,"title":"Homogenes LGS nur trivial lösbar ⇔ det A ≠ 0","note":null,"deps":["L:11.8","L:8.23","L:12.17"],"links":["L:11.8","L:8.23","L:12.17"],"implied":[],"depth":22,"weight":0,"pos":[6191,2597.6,6],"landmark":false,"img":{"s":[983,99],"p":[983,345]}},{"id":"L:12.22","label":"12.22","course":"L","kind":"Satz","chapter":"12","name":"Cramersche Regel","page":148,"title":"Cramersche Regel","note":null,"deps":["L:12.7","L:12.17"],"links":["L:12.17"],"implied":[{"id":"L:12.7","via":"L:12.17"}],"depth":22,"weight":0,"pos":[6317.5,2570.6,6],"landmark":false,"img":{"s":[983,225],"p":[983,333]}},{"id":"L:13.7","label":"13.7","course":"L","kind":"Satz","chapter":"13","name":null,"page":153,"title":"Eigenwerte = Nullstellen des charakteristischen Polynoms","note":null,"deps":["L:13.1","L:13.5","L:12.17","L:12.10"],"links":["L:13.1","L:13.5","L:12.17"],"implied":[{"id":"L:12.10","via":"L:12.17"}],"depth":22,"weight":47,"pos":[6237.4,2467.1,16.3],"landmark":true,"img":{"s":[983,144]}},{"id":"2:III.33","label":"III.33","course":"2","kind":"Satz","chapter":"III","name":"Satz von Fubini","page":52,"title":"Satz von Fubini (stetige Funktionen auf Rechtecken)","note":null,"deps":["2:III.31","2:III.32","1:XI.3"],"links":["2:III.32"],"implied":[{"id":"2:III.31","via":"2:III.32"},{"id":"1:XI.3","via":"2:III.32"}],"depth":23,"weight":0,"pos":[4162.8,5478,6],"landmark":false,"img":{"s":[983,334],"p":[983,2421]}},{"id":"2:III.34","label":"III.34","course":"2","kind":"Lemma","chapter":"III","name":null,"page":54,"title":"Erste Variation","note":null,"deps":["2:III.32","2:II.11"],"links":["2:III.32","2:II.11"],"implied":[],"depth":23,"weight":1,"pos":[4200.8,5453,7.5],"landmark":false,"img":{"s":[983,658],"p":[983,680]}},{"id":"1:V.14","label":"V.14","course":"1","kind":"Satz","chapter":"V","name":null,"page":66,"title":"exp(z) = lim (1 + z/n)ⁿ","note":"Benutzt eine Identität aus Übungsblatt 7","deps":["1:V.exp","1:II.15","1:III.7"],"links":["1:V.exp","1:II.15"],"implied":[{"id":"1:III.7","via":"1:V.exp"}],"depth":23,"weight":0,"pos":[499.7,3529.8,6],"landmark":false,"img":{"s":[983,199],"p":[983,1212]}},{"id":"1:V.17","label":"V.17","course":"1","kind":"Satz","chapter":"V","name":null,"page":68,"title":"Eigenschaften von exp","note":null,"deps":["1:V.15","1:V.exp","1:II.15","1:V.16","1:IV.22"],"links":["1:V.15","1:V.exp","1:II.15","1:V.16"],"implied":[{"id":"1:IV.22","via":"1:V.15"}],"depth":23,"weight":33,"pos":[475.8,3594.9,14.6],"landmark":false,"img":{"s":[983,385],"p":[983,1210]}},{"id":"2:VI.22","label":"VI.22","course":"2","kind":"Definition","chapter":"VI","name":null,"page":124,"title":"Matrix-Exponentialfunktion","note":null,"deps":["1:V.exp","1:V.5","L:5.52"],"links":["1:V.exp","1:V.5","L:5.52"],"implied":[],"depth":23,"weight":5,"pos":[4451.4,5444.8,9.4],"landmark":false,"img":{"s":[983,339]}},{"id":"1:IX.5","label":"IX.5","course":"1","kind":"Satz","chapter":"IX","name":null,"page":112,"title":"Potenzreihen sind stetig","note":null,"deps":["1:IX.2","1:V.11","1:V.10","1:V.9"],"links":["1:IX.2","1:V.11","1:V.10"],"implied":[{"id":"1:V.9","via":"1:V.11"}],"depth":23,"weight":10,"pos":[2852.2,3431.8,10.7],"landmark":false,"img":{"s":[983,81],"p":[983,908]}},{"id":"3:II.3","label":"II.3","course":"3","kind":"Satz","chapter":"II","name":null,"page":18,"title":"Konstruktion äußerer Maße aus Überdeckungen","note":null,"deps":["3:II.1","1:V.6"],"links":["3:II.1","1:V.6"],"implied":[],"depth":23,"weight":48,"pos":[4463,7465.9,16.4],"landmark":false,"img":{"s":[983,230],"p":[983,450]}},{"id":"1:V.13","label":"V.13","course":"1","kind":"Satz","chapter":"V","name":"Identitätssatz für Potenzreihen","page":65,"title":"Identitätssatz für Potenzreihen","note":null,"deps":["1:V.12","1:V.10"],"links":["1:V.12","1:V.10"],"implied":[],"depth":23,"weight":0,"pos":[312.6,3609.4,6],"landmark":false,"img":{"s":[983,157],"p":[983,297]}},{"id":"3:II.4","label":"II.4","course":"3","kind":"Satz","chapter":"II","name":null,"page":18,"title":"Einschränkung eines äußeren Maßes","note":null,"deps":["3:II.1","3:II.2"],"links":["3:II.2"],"implied":[{"id":"3:II.1","via":"3:II.2"}],"depth":23,"weight":0,"pos":[4485.1,7678.1,6],"landmark":false,"img":{"s":[983,193],"p":[983,419]}},{"id":"3:II.5","label":"II.5","course":"3","kind":"Satz","chapter":"II","name":null,"page":19,"title":"Nullmengen sind messbar","note":null,"deps":["3:II.1","3:II.2"],"links":["3:II.2"],"implied":[{"id":"3:II.1","via":"3:II.2"}],"depth":23,"weight":63,"pos":[4533,7649.4,17.9],"landmark":false,"img":{"s":[983,159],"p":[983,649]}},{"id":"3:II.6","label":"II.6","course":"3","kind":"Lemma","chapter":"II","name":null,"page":19,"title":"Additivität auf messbaren Mengen","note":null,"deps":["3:II.2","1:II.3"],"links":["3:II.2","1:II.3"],"implied":[],"depth":23,"weight":63,"pos":[4368.6,7683,17.9],"landmark":false,"img":{"s":[983,161],"p":[983,703]}},{"id":"3:I.10","label":"I.10","course":"3","kind":"Satz","chapter":"I","name":null,"page":8,"title":"Minimalität der Vervollständigung","note":null,"deps":["3:I.9"],"links":["3:I.9"],"implied":[],"depth":23,"weight":43,"pos":[3139.4,7575.4,15.8],"landmark":false,"img":{"s":[983,237],"p":[983,141]}},{"id":"3:I.19","label":"I.19","course":"3","kind":"Lemma","chapter":"I","name":null,"page":14,"title":"Fast überall gleich ⇒ messbar","note":null,"deps":["3:I.18","3:I.14","3:I.8"],"links":["3:I.18","3:I.14"],"implied":[{"id":"3:I.8","via":"3:I.18"}],"depth":23,"weight":1,"pos":[3122.2,7631,7.5],"landmark":false,"img":{"s":[983,70],"p":[983,722]}},{"id":"3:I.21","label":"I.21","course":"3","kind":"Satz","chapter":"I","name":"Egorov","page":15,"title":"Satz von Egorov","note":null,"deps":["3:I.17","3:I.7","3:I.18"],"links":["3:I.17","3:I.7","3:I.18"],"implied":[],"depth":23,"weight":2,"pos":[3095,7757.9,8.1],"landmark":false,"img":{"s":[983,210],"p":[983,1626]}},{"id":"3:IV.1","label":"IV.1","course":"3","kind":"Definition","chapter":"IV","name":null,"page":47,"title":"µ-Treppenfunktion","note":null,"deps":["3:I.18","L:6.1"],"links":["3:I.18"],"implied":[{"id":"L:6.1","via":"3:I.18"}],"depth":23,"weight":56,"pos":[2542.8,7937.4,17.2],"landmark":false,"img":{"s":[983,640]}},{"id":"3:VI.6","label":"VI.6","course":"3","kind":"Definition","chapter":"VI","name":null,"page":82,"title":"σ-endliche Funktion","note":null,"deps":["3:I.6","3:I.18"],"links":["3:I.6","3:I.18"],"implied":[],"depth":23,"weight":15,"pos":[3331.3,8190.3,11.8],"landmark":false,"img":{"s":[983,240]}},{"id":"3:II.27","label":"II.27","course":"3","kind":"Satz","chapter":"II","name":null,"page":30,"title":"Fortsetzung eines Inhalts auf den Ring","note":null,"deps":["3:II.25","3:II.26"],"links":["3:II.25","3:II.26"],"implied":[],"depth":23,"weight":44,"pos":[4304.1,7669.7,15.9],"landmark":false,"img":{"s":[983,70],"p":[983,641]}},{"id":"3:II.29","label":"II.29","course":"3","kind":"Satz","chapter":"II","name":null,"page":31,"title":"Das Volumen ist ein Inhalt auf den Quadern","note":null,"deps":["3:II.22","3:II.26"],"links":["3:II.22","3:II.26"],"implied":[],"depth":23,"weight":41,"pos":[4433.4,7692.4,15.6],"landmark":false,"img":{"s":[983,42],"p":[983,1116]}},{"id":"3:II.32","label":"II.32","course":"3","kind":"Satz","chapter":"II","name":null,"page":33,"title":"Prämaß ⇔ Stetigkeit von unten/oben","note":null,"deps":["3:I.7","3:II.26","3:II.11"],"links":["3:I.7","3:II.26"],"implied":[{"id":"3:II.11","via":"3:II.26"}],"depth":23,"weight":0,"pos":[4467.3,7637.8,6],"landmark":false,"img":{"s":[983,608],"p":[983,1637]}},{"id":"2:V.5","label":"V.5","course":"2","kind":"Definition","chapter":"V","name":"Parametrisierung nach der Bogenlänge","page":79,"title":"Parametrisierung nach der Bogenlänge","note":null,"deps":["2:V.2"],"links":["2:V.2"],"implied":[],"depth":23,"weight":1,"pos":[4969.7,5199.8,7.5],"landmark":false,"img":{"s":[983,374]}},{"id":"2:V.7","label":"V.7","course":"2","kind":"Definition","chapter":"V","name":null,"page":80,"title":"Stückweise C¹-Kurven","note":null,"deps":["2:V.1","2:V.2"],"links":["2:V.2"],"implied":[{"id":"2:V.1","via":"2:V.2"}],"depth":23,"weight":21,"pos":[5065.9,5200.9,12.9],"landmark":false,"img":{"s":[983,567]}},{"id":"1:VIII.14","label":"VIII.14","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":101,"title":"Monotonie über das Vorzeichen von f′","note":null,"deps":["1:VIII.13"],"links":["1:VIII.13"],"implied":[],"depth":23,"weight":108,"pos":[2245.9,3509.3,21.6],"landmark":false,"img":{"s":[983,290],"p":[983,289]}},{"id":"1:VIII.23","label":"VIII.23","course":"1","kind":"Satz","chapter":"VIII","name":"Verallgemeinerter Mittelwertsatz","page":106,"title":"Verallgemeinerter Mittelwertsatz","note":null,"deps":["1:VIII.13"],"links":["1:VIII.13"],"implied":[],"depth":23,"weight":1,"pos":[2306.8,3514.1,7.5],"landmark":false,"img":{"s":[983,216],"p":[983,387]}},{"id":"2:II.4","label":"II.4","course":"2","kind":"Satz","chapter":"II","name":"Satz von Schwarz","page":16,"title":"Satz von Schwarz","note":null,"deps":["2:II.3","2:II.1","1:VIII.13"],"links":["2:II.3","1:VIII.13"],"implied":[{"id":"2:II.1","via":"2:II.3"}],"depth":23,"weight":26,"pos":[3422.5,5268.8,13.6],"landmark":true,"img":{"s":[983,122],"p":[983,1398]}},{"id":"2:II.8","label":"II.8","course":"2","kind":"Satz","chapter":"II","name":null,"page":19,"title":"Ableitung, Richtungsableitungen, Jacobimatrix","note":null,"deps":["2:II.7","2:II.6","2:II.2"],"links":["2:II.7","2:II.6","2:II.2"],"implied":[],"depth":23,"weight":84,"pos":[3469.2,5223.1,19.7],"landmark":false,"img":{"s":[983,365],"p":[983,2806]}},{"id":"L:18.40","label":"18.40","course":"L","kind":"Satz","chapter":"18","name":"Eigenschaften der Orthogonalprojektion","page":208,"title":"Eigenschaften der Orthogonalprojektion","note":null,"deps":["L:18.39","L:9.1"],"links":["L:18.39","L:9.1"],"implied":[],"depth":23,"weight":1,"pos":[7028.7,2241.9,7.5],"landmark":false,"img":{"s":[983,275],"p":[983,201]}},{"id":"L:19.7","label":"19.7","course":"L","kind":"Lemma","chapter":"19","name":"Matrix eines s.a. Endomorphismus","page":221,"title":"Selbstadjungiert ⇔ symmetrische/hermitesche Matrix","note":null,"deps":["L:19.5","L:19.2"],"links":["L:19.5","L:19.2"],"implied":[],"depth":23,"weight":34,"pos":[7170.9,2769.8,14.7],"landmark":false,"img":{"s":[983,134],"p":[983,271]}},{"id":"L:19.22","label":"19.22","course":"L","kind":"Satz","chapter":"19","name":"Lineare Isometrien und Adjungierte","page":230,"title":"Isometrie ⇔ Φ*Φ = id","note":null,"deps":["L:19.20","L:19.2"],"links":["L:19.20","L:19.2"],"implied":[],"depth":23,"weight":6,"pos":[7110.2,2775.1,9.7],"landmark":false,"img":{"s":[983,378],"p":[983,452]}},{"id":"L:20.14","label":"20.14","course":"L","kind":"Satz","chapter":"20","name":"Interpretation Nullraum","page":248,"title":"Nullraum = Kern von Φ","note":null,"deps":["L:20.11","L:20.9"],"links":["L:20.11","L:20.9"],"implied":[],"depth":23,"weight":9,"pos":[6893.1,2938,10.5],"landmark":false,"img":{"s":[983,215],"p":[983,493]}},{"id":"L:18.57","label":"18.57","course":"L","kind":"Satz","chapter":"18","name":"Iwasawa–Zerlegung","page":216,"title":"Iwasawa-Zerlegung","note":null,"deps":["L:18.33","L:18.54"],"links":["L:18.33","L:18.54"],"implied":[],"depth":23,"weight":0,"pos":[7170.8,2308.2,6],"landmark":false,"img":{"s":[983,318],"p":[983,1181]}},{"id":"L:12.19","label":"12.19","course":"L","kind":"Definition","chapter":"12","name":null,"page":147,"title":"Determinante eines Endomorphismus","note":null,"deps":["L:12.18","L:10.1"],"links":["L:12.18"],"implied":[{"id":"L:10.1","via":"L:12.18"}],"depth":23,"weight":0,"pos":[6256.9,2661.2,6],"landmark":false,"img":{"s":[983,392]}},{"id":"L:14.6","label":"14.6","course":"L","kind":"Satz","chapter":"14","name":"2. Kriterium für Diagonalisierbarkeit eines Endomorphismus","page":157,"title":"2. Kriterium: geometrische = algebraische Vielfachheit","note":null,"deps":["L:14.3","L:13.7","L:13.4"],"links":["L:14.3","L:13.7"],"implied":[{"id":"L:13.4","via":"L:14.3"}],"depth":23,"weight":0,"pos":[5510.3,3111.7,6],"landmark":true,"img":{"s":[983,313]}},{"id":"L:15.2","label":"15.2","course":"L","kind":"Satz","chapter":"15","name":null,"page":161,"title":"Trigonalisierbar ⇔ charakteristisches Polynom zerfällt","note":null,"deps":["L:15.1","L:13.7","L:8.27","1:II.3"],"links":["L:15.1","L:13.7","L:8.27"],"implied":[{"id":"1:II.3","via":"L:13.7"}],"depth":23,"weight":3,"pos":[4884.1,3261.8,8.6],"landmark":false,"img":{"s":[983,70],"p":[983,1197]}},{"id":"L:17.7","label":"17.7","course":"L","kind":"Lemma","chapter":"17","name":null,"page":170,"title":"Charakteristisches Polynom auf dem Hauptraum","note":null,"deps":["L:17.6","L:13.7","L:12.16"],"links":["L:17.6","L:13.7"],"implied":[{"id":"L:12.16","via":"L:13.7"}],"depth":23,"weight":8,"pos":[6289,3095.6,10.2],"landmark":false,"img":{"s":[983,248],"p":[983,458]}},{"id":"1:V.18","label":"V.18","course":"1","kind":"Definition","chapter":"V","name":null,"page":69,"title":"cos und sin","note":null,"deps":["1:V.17","1:V.exp"],"links":["1:V.17"],"implied":[{"id":"1:V.exp","via":"1:V.17"}],"depth":24,"weight":28,"pos":[417.6,3673.7,13.9],"landmark":false,"img":{"s":[983,436]}},{"id":"1:VI.9","label":"VI.9","course":"1","kind":"Satz","chapter":"VI","name":null,"page":77,"title":"exp ist stetig","note":null,"deps":["1:V.exp","1:V.17","1:VI.3"],"links":["1:V.17","1:VI.3"],"implied":[{"id":"1:V.exp","via":"1:V.17"}],"depth":24,"weight":11,"pos":[1927.8,3239.9,11],"landmark":false,"img":{"s":[983,40],"p":[983,684]}},{"id":"3:II.7","label":"II.7","course":"3","kind":"Satz","chapter":"II","name":null,"page":20,"title":"M(µ) ist σ-Algebra, µ ist dort ein vollständiges Maß","note":null,"deps":["3:II.6","3:II.5","3:I.7","3:I.1","3:I.5","3:I.8"],"links":["3:II.6","3:II.5","3:I.8"],"implied":[{"id":"3:I.7","via":"3:II.6"},{"id":"3:I.1","via":"3:II.6"},{"id":"3:I.5","via":"3:II.6"}],"depth":24,"weight":62,"pos":[4322.6,7732.8,17.8],"landmark":false,"img":{"s":[983,70],"p":[983,2257]}},{"id":"3:I.20","label":"I.20","course":"3","kind":"Satz","chapter":"I","name":null,"page":15,"title":"Fast überall punktweise Grenzwerte sind messbar","note":null,"deps":["3:I.19","3:I.16","3:I.14"],"links":["3:I.19","3:I.16"],"implied":[{"id":"3:I.14","via":"3:I.19"}],"depth":24,"weight":0,"pos":[3070.5,7679.1,6],"landmark":false,"img":{"s":[983,70],"p":[983,374]}},{"id":"3:IV.2","label":"IV.2","course":"3","kind":"Lemma","chapter":"IV","name":null,"page":47,"title":"Integral von Treppenfunktionen","note":null,"deps":["3:IV.1","3:I.5"],"links":["3:IV.1"],"implied":[{"id":"3:I.5","via":"3:IV.1"}],"depth":24,"weight":54,"pos":[2532.4,8002.8,17],"landmark":false,"img":{"s":[983,385],"p":[983,1502]}},{"id":"3:IV.9","label":"IV.9","course":"3","kind":"Satz","chapter":"IV","name":null,"page":52,"title":"Approximation durch Treppenfunktionen","note":null,"deps":["3:IV.1","3:I.17"],"links":["3:IV.1","3:I.17"],"implied":[],"depth":24,"weight":40,"pos":[2673.9,8152.8,15.5],"landmark":false,"img":{"s":[983,109],"p":[983,960]}},{"id":"3:II.28","label":"II.28","course":"3","kind":"Lemma","chapter":"II","name":null,"page":30,"title":"Inhalte sind monoton und subadditiv","note":null,"deps":["3:II.27"],"links":["3:II.27"],"implied":[],"depth":24,"weight":41,"pos":[4386.9,7745.9,15.6],"landmark":false,"img":{"s":[983,67],"p":[983,691]}},{"id":"3:II.30","label":"II.30","course":"3","kind":"Satz","chapter":"II","name":null,"page":32,"title":"Prämaß auf Halbring ⇒ Prämaß auf Ring","note":null,"deps":["3:II.27","3:II.25","3:II.3"],"links":["3:II.27","3:II.3"],"implied":[{"id":"3:II.25","via":"3:II.27"}],"depth":24,"weight":41,"pos":[4482.9,7731.7,15.6],"landmark":false,"img":{"s":[983,100],"p":[983,1233]}},{"id":"2:V.6","label":"V.6","course":"2","kind":"Satz","chapter":"V","name":"Parametrisierung nach der Bogenlänge","page":79,"title":"Existenz der Bogenlängen-Parametrisierung","note":null,"deps":["2:V.5","2:V.2","1:VIII.8","1:XI.3","1:VII.7"],"links":["2:V.5","1:VIII.8","1:XI.3"],"implied":[{"id":"2:V.2","via":"2:V.5"},{"id":"1:VII.7","via":"1:VIII.8"}],"depth":24,"weight":0,"pos":[5060.9,5262.8,6],"landmark":false,"img":{"s":[983,123],"p":[983,882]}},{"id":"2:V.8","label":"V.8","course":"2","kind":"Definition","chapter":"V","name":null,"page":80,"title":"Kurvenintegral eines Vektorfeldes","note":null,"deps":["2:V.7","1:X.3","1:IV.9"],"links":["2:V.7","1:IV.9"],"implied":[{"id":"1:X.3","via":"2:V.7"}],"depth":24,"weight":18,"pos":[5010.6,5263.3,12.4],"landmark":false,"img":{"s":[983,1600]}},{"id":"2:V.16","label":"V.16","course":"2","kind":"Definition","chapter":"V","name":"Homotopie","page":86,"title":"Homotopie von Kurven","note":null,"deps":["2:V.7","2:I.17"],"links":["2:V.7","2:I.17"],"implied":[],"depth":24,"weight":12,"pos":[4921.9,5268.8,11.2],"landmark":false,"img":{"s":[983,361]}},{"id":"1:VIII.16","label":"VIII.16","course":"1","kind":"Satz","chapter":"VIII","name":"Schrankensatz","page":101,"title":"Schrankensatz","note":null,"deps":["1:VIII.14","1:VIII.6"],"links":["1:VIII.14"],"implied":[{"id":"1:VIII.6","via":"1:VIII.14"}],"depth":24,"weight":12,"pos":[2181.9,3587.2,11.2],"landmark":false,"img":{"s":[983,230],"p":[983,763]}},{"id":"1:VIII.20","label":"VIII.20","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":104,"title":"Hinreichendes Kriterium f″ > 0","note":null,"deps":["1:VIII.14","1:VIII.18","1:VIII.11","1:VI.15"],"links":["1:VIII.14","1:VIII.18"],"implied":[{"id":"1:VIII.11","via":"1:VIII.14"},{"id":"1:VI.15","via":"1:VIII.14"}],"depth":24,"weight":3,"pos":[2278.2,3562.4,8.6],"landmark":false,"img":{"s":[983,243],"p":[983,502]}},{"id":"1:VIII.22","label":"VIII.22","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":105,"title":"Charakterisierungen der Konvexität","note":null,"deps":["1:VIII.21","1:VIII.12","1:VII.3","1:VIII.14","1:VIII.19"],"links":["1:VIII.21","1:VIII.14","1:VIII.19"],"implied":[{"id":"1:VIII.12","via":"1:VIII.14"},{"id":"1:VII.3","via":"1:VIII.14"}],"depth":24,"weight":2,"pos":[2230,3569.4,8.1],"landmark":false,"img":{"s":[983,329],"p":[983,1925]}},{"id":"1:XI.2","label":"XI.2","course":"1","kind":"Satz","chapter":"XI","name":null,"page":127,"title":"Stammfunktionen unterscheiden sich um Konstanten","note":null,"deps":["1:XI.1","1:VIII.14"],"links":["1:XI.1","1:VIII.14"],"implied":[],"depth":24,"weight":80,"pos":[3775.3,3707.8,19.4],"landmark":false,"img":{"s":[983,76],"p":[983,1061]}},{"id":"2:I.26","label":"I.26","course":"2","kind":"Satz","chapter":"I","name":null,"page":11,"title":"Zusammenhängend in ℝ ⇔ Intervall","note":null,"deps":["2:I.25","1:VIII.14","1:I.11"],"links":["2:I.25","1:VIII.14"],"implied":[{"id":"1:I.11","via":"2:I.25"}],"depth":24,"weight":17,"pos":[2627.2,5322.9,12.2],"landmark":false,"img":{"s":[983,62],"p":[983,407]}},{"id":"2:VI.12","label":"VI.12","course":"2","kind":"Lemma","chapter":"VI","name":"Gronwall","page":113,"title":"Lemma von Gronwall","note":null,"deps":["1:XI.3","1:VIII.14"],"links":["1:XI.3","1:VIII.14"],"implied":[],"depth":24,"weight":11,"pos":[4524.5,5463.5,11],"landmark":true,"img":{"s":[983,602],"p":[983,350]}},{"id":"3:V.10","label":"V.10","course":"3","kind":"Lemma","chapter":"V","name":"Youngsche Ungleichung","page":65,"title":"Youngsche Ungleichung","note":null,"deps":["1:VIII.14"],"links":["1:VIII.14"],"implied":[],"depth":24,"weight":18,"pos":[4770.6,8090.3,12.4],"landmark":false,"img":{"s":[983,120],"p":[983,543]}},{"id":"1:VIII.24","label":"VIII.24","course":"1","kind":"Satz","chapter":"VIII","name":"L’Hospitalsche Regeln","page":107,"title":"Regeln von L'Hospital","note":null,"deps":["1:VIII.23","1:VI.15"],"links":["1:VIII.23"],"implied":[{"id":"1:VI.15","via":"1:VIII.23"}],"depth":24,"weight":0,"pos":[2194.7,3539.7,6],"landmark":true,"img":{"s":[983,415],"p":[983,2450]}},{"id":"2:II.5","label":"II.5","course":"2","kind":"Lemma","chapter":"II","name":null,"page":17,"title":"Partielle Ableitungen bis Ordnung k vertauschen","note":null,"deps":["2:II.4","L:5.17"],"links":["2:II.4","L:5.17"],"implied":[],"depth":24,"weight":4,"pos":[3418.5,5352,9],"landmark":false,"img":{"s":[983,123],"p":[983,952]}},{"id":"2:III.12","label":"III.12","course":"2","kind":"Definition","chapter":"III","name":null,"page":34,"title":"Zweite Ableitung, Hessematrix","note":null,"deps":["2:II.3","2:II.4"],"links":["2:II.4"],"implied":[{"id":"2:II.3","via":"2:II.4"}],"depth":24,"weight":5,"pos":[4175.2,5338.1,9.4],"landmark":false,"img":{"s":[983,689]}},{"id":"3:IX.10","label":"IX.10","course":"3","kind":"Lemma","chapter":"IX","name":null,"page":115,"title":"Rotation unter Parametrisierung","note":null,"deps":["2:II.11","2:II.4"],"links":["2:II.11","2:II.4"],"implied":[],"depth":24,"weight":1,"pos":[3784.3,8135.7,7.5],"landmark":false,"img":{"s":[983,109],"p":[983,5326]}},{"id":"2:II.9","label":"II.9","course":"2","kind":"Definition","chapter":"II","name":"Gradient","page":21,"title":"Gradient","note":null,"deps":["2:II.7","2:II.8","1:IV.9"],"links":["2:II.8"],"implied":[{"id":"2:II.7","via":"2:II.8"},{"id":"1:IV.9","via":"2:II.8"}],"depth":24,"weight":12,"pos":[3455.5,5315.1,11.2],"landmark":false,"img":{"s":[983,2019]}},{"id":"2:II.14","label":"II.14","course":"2","kind":"Satz","chapter":"II","name":null,"page":26,"title":"Stetige partielle Ableitungen ⇒ differenzierbar","note":null,"deps":["2:II.12","2:II.8","1:VIII.13"],"links":["2:II.12","2:II.8","1:VIII.13"],"implied":[],"depth":24,"weight":70,"pos":[3374.7,5311.7,18.5],"landmark":false,"img":{"s":[983,97],"p":[983,777]}},{"id":"2:III.10","label":"III.10","course":"2","kind":"Satz","chapter":"III","name":null,"page":33,"title":"Lokales Extremum ⇒ Df = 0","note":null,"deps":["2:III.9","2:II.8","1:VIII.12"],"links":["2:III.9","2:II.8","1:VIII.12"],"implied":[],"depth":24,"weight":4,"pos":[4127.2,5323,9],"landmark":false,"img":{"s":[983,70],"p":[983,143]}},{"id":"L:18.44","label":"18.44","course":"L","kind":"Satz","chapter":"18","name":"Kürzester Abstand","page":210,"title":"Kürzester Abstand durch Projektion","note":null,"deps":["L:18.40","L:18.27","L:18.43"],"links":["L:18.40","L:18.27","L:18.43"],"implied":[],"depth":24,"weight":0,"pos":[7126.9,2306.2,6],"landmark":false,"img":{"s":[983,605],"p":[983,612]}},{"id":"L:19.8","label":"19.8","course":"L","kind":"Satz","chapter":"19","name":null,"page":222,"title":"Selbstadjungierte haben reelle Eigenwerte","note":null,"deps":["L:19.7","L:13.7","L:13.8"],"links":["L:19.7","L:13.7","L:13.8"],"implied":[],"depth":24,"weight":33,"pos":[7067.6,3029.1,14.6],"landmark":false,"img":{"s":[983,278],"p":[983,654]}},{"id":"L:19.23","label":"19.23","course":"L","kind":"Korollar","chapter":"19","name":null,"page":230,"title":"Isometrie ⇔ Φ* = Φ⁻¹, Matrix orthogonal/unitär","note":null,"deps":["L:19.22","L:18.50"],"links":["L:19.22","L:18.50"],"implied":[],"depth":24,"weight":5,"pos":[7149.1,2821.5,9.4],"landmark":false,"img":{"s":[983,172],"p":[983,253]}},{"id":"L:15.3","label":"15.3","course":"L","kind":"Korollar","chapter":"15","name":null,"page":162,"title":"Über ℂ ist jeder Endomorphismus trigonalisierbar","note":null,"deps":["L:15.2","L:13.8"],"links":["L:15.2","L:13.8"],"implied":[],"depth":24,"weight":2,"pos":[4911.6,3337.8,8.1],"landmark":false,"img":{"s":[983,67],"p":[983,101]}},{"id":"L:17.8","label":"17.8","course":"L","kind":"Satz","chapter":"17","name":"Hauptraumzerlegung","page":171,"title":"Hauptraumzerlegung","note":null,"deps":["L:17.6","L:17.7","L:13.8"],"links":["L:17.7","L:13.8"],"implied":[{"id":"L:17.6","via":"L:17.7"}],"depth":24,"weight":7,"pos":[6286.3,3162,10],"landmark":false,"img":{"s":[983,291],"p":[983,494]}},{"id":"1:V.19","label":"V.19","course":"1","kind":"Lemma","chapter":"V","name":null,"page":69,"title":"Additionstheoreme","note":null,"deps":["1:V.18","1:V.17","1:IV.21"],"links":["1:V.18"],"implied":[{"id":"1:V.17","via":"1:V.18"},{"id":"1:IV.21","via":"1:V.18"}],"depth":25,"weight":9,"pos":[397.5,3726.4,10.5],"landmark":false,"img":{"s":[983,353],"p":[983,749]}},{"id":"1:V.20","label":"V.20","course":"1","kind":"Satz","chapter":"V","name":null,"page":70,"title":"Reihendarstellung von cos und sin","note":null,"deps":["1:V.18","1:V.exp","1:V.5","1:V.4"],"links":["1:V.18","1:V.5"],"implied":[{"id":"1:V.exp","via":"1:V.18"},{"id":"1:V.4","via":"1:V.18"}],"depth":25,"weight":9,"pos":[308.3,3715.2,10.5],"landmark":false,"img":{"s":[983,250],"p":[983,621]}},{"id":"1:V.21","label":"V.21","course":"1","kind":"Lemma","chapter":"V","name":null,"page":71,"title":"∣sin t − t∣ ≤ t²","note":null,"deps":["1:V.exp","1:V.18"],"links":["1:V.18"],"implied":[{"id":"1:V.exp","via":"1:V.18"}],"depth":25,"weight":0,"pos":[350.7,3738.9,6],"landmark":false,"img":{"s":[983,105],"p":[983,317]}},{"id":"1:VII.9","label":"VII.9","course":"1","kind":"Satz","chapter":"VII","name":null,"page":85,"title":"exp und log","note":null,"deps":["1:VI.9","1:VII.7","1:V.17","1:V.exp","1:III.11"],"links":["1:VI.9","1:VII.7","1:III.11"],"implied":[{"id":"1:V.17","via":"1:VI.9"},{"id":"1:V.exp","via":"1:VI.9"}],"depth":25,"weight":10,"pos":[1231.1,3764.1,10.7],"landmark":false,"img":{"s":[983,458],"p":[983,1134]}},{"id":"3:II.8","label":"II.8","course":"3","kind":"Lemma","chapter":"II","name":null,"page":22,"title":"Stetigkeit äußerer Maße auf messbaren Mengen","note":null,"deps":["3:I.7","3:II.7"],"links":["3:II.7"],"implied":[{"id":"3:I.7","via":"3:II.7"}],"depth":25,"weight":34,"pos":[4292.5,7794.1,14.7],"landmark":false,"img":{"s":[983,351],"p":[983,42]}},{"id":"3:II.13","label":"II.13","course":"3","kind":"Satz","chapter":"II","name":"Caratheodory-Fortsetzung","page":23,"title":"Carathéodory-Fortsetzung","note":null,"deps":["3:II.3","3:II.11","3:II.12","3:II.7"],"links":["3:II.3","3:II.12","3:II.7"],"implied":[{"id":"3:II.11","via":"3:II.12"}],"depth":25,"weight":46,"pos":[4455.8,7789.4,16.2],"landmark":true,"img":{"s":[983,321],"p":[983,760]}},{"id":"3:IV.3","label":"IV.3","course":"3","kind":"Definition","chapter":"IV","name":"Lebesgue-Integral","page":49,"title":"Lebesgue-Integral","note":null,"deps":["3:IV.2","3:I.18"],"links":["3:IV.2"],"implied":[{"id":"3:I.18","via":"3:IV.2"}],"depth":25,"weight":53,"pos":[2635.2,8060.7,16.9],"landmark":true,"img":{"s":[983,360]}},{"id":"3:III.1","label":"III.1","course":"3","kind":"Lemma","chapter":"III","name":null,"page":35,"title":"Das Volumen ist ein Prämaß","note":null,"deps":["3:II.27","3:II.28","3:II.29","1:IV.20"],"links":["3:II.28","3:II.29","1:IV.20"],"implied":[{"id":"3:II.27","via":"3:II.28"}],"depth":25,"weight":40,"pos":[2822,8717.4,15.5],"landmark":false,"img":{"s":[983,70],"p":[983,554]}},{"id":"2:V.10","label":"V.10","course":"2","kind":"Lemma","chapter":"V","name":null,"page":82,"title":"Abschätzung des Kurvenintegrals","note":null,"deps":["2:V.8","2:V.2","1:IV.11","1:X.8"],"links":["2:V.8","1:IV.11","1:X.8"],"implied":[{"id":"2:V.2","via":"2:V.8"}],"depth":25,"weight":4,"pos":[5051.7,5368.9,9],"landmark":false,"img":{"s":[983,366],"p":[983,580]}},{"id":"2:V.24","label":"V.24","course":"2","kind":"Definition","chapter":"V","name":null,"page":92,"title":"Integral einer 1-Form","note":null,"deps":["2:V.23","2:V.8"],"links":["2:V.23","2:V.8"],"implied":[],"depth":25,"weight":1,"pos":[4990.6,5311.1,7.5],"landmark":false,"img":{"s":[983,777]}},{"id":"2:V.29","label":"V.29","course":"2","kind":"Definition","chapter":"V","name":null,"page":95,"title":"Komplexes Kurvenintegral","note":null,"deps":["2:V.8","1:IV.C"],"links":["2:V.8","1:IV.C"],"implied":[],"depth":25,"weight":5,"pos":[5038.6,5320.3,9.4],"landmark":false,"img":{"s":[983,1079]}},{"id":"2:V.17","label":"V.17","course":"2","kind":"Lemma","chapter":"V","name":null,"page":86,"title":"Ableitung des Kurvenintegrals längs einer Homotopie","note":null,"deps":["2:V.16","2:V.8","2:II.4","2:III.32"],"links":["2:V.16","2:V.8","2:II.4","2:III.32"],"implied":[],"depth":25,"weight":10,"pos":[4984.5,5550.7,10.7],"landmark":false,"img":{"s":[983,323],"p":[983,935]}},{"id":"2:V.21","label":"V.21","course":"2","kind":"Definition","chapter":"V","name":null,"page":90,"title":"Einfach zusammenhängend","note":null,"deps":["2:V.16","2:III.3"],"links":["2:V.16","2:III.3"],"implied":[],"depth":25,"weight":2,"pos":[4958.4,5346.2,8.1],"landmark":false,"img":{"s":[983,412]}},{"id":"1:VIII.17","label":"VIII.17","course":"1","kind":"Lemma","chapter":"VIII","name":null,"page":102,"title":"Schrankensatz für vektorwertige Funktionen","note":null,"deps":["1:VIII.16","1:IV.11","1:VIII.2"],"links":["1:VIII.16","1:VIII.2"],"implied":[{"id":"1:IV.11","via":"1:VIII.16"}],"depth":25,"weight":11,"pos":[2218.2,3627.4,11],"landmark":false,"img":{"s":[983,214],"p":[983,744]}},{"id":"1:XI.4","label":"XI.4","course":"1","kind":"Lemma","chapter":"XI","name":null,"page":128,"title":"F(x) = F(x₀) + ∫f","note":null,"deps":["1:XI.2","1:XI.3","1:X.8","1:VI.1"],"links":["1:XI.2","1:XI.3"],"implied":[{"id":"1:X.8","via":"1:XI.3"},{"id":"1:VI.1","via":"1:XI.2"}],"depth":25,"weight":79,"pos":[3719.6,3751.5,19.3],"landmark":false,"img":{"s":[983,131],"p":[983,478]}},{"id":"2:I.28","label":"I.28","course":"2","kind":"Lemma","chapter":"I","name":null,"page":12,"title":"Zwischenwertsatz, allgemein","note":"Kein eigener Beweis: folgt aus I.26 und I.27","deps":["2:I.26","2:I.27"],"links":["2:I.26","2:I.27"],"implied":[],"depth":25,"weight":0,"pos":[2505.1,5367.4,6],"landmark":false,"img":{"s":[983,1247]}},{"id":"2:III.5","label":"III.5","course":"2","kind":"Satz","chapter":"III","name":null,"page":30,"title":"Wegzusammenhang und Zusammenhang","note":null,"deps":["2:III.3","2:I.24","2:I.25","2:I.26"],"links":["2:III.3","2:I.26"],"implied":[{"id":"2:I.24","via":"2:I.25"},{"id":"2:I.25","via":"2:I.26"}],"depth":25,"weight":1,"pos":[4033.1,5466.2,7.5],"landmark":false,"img":{"s":[983,404],"p":[983,1168]}},{"id":"2:III.13","label":"III.13","course":"2","kind":"Lemma","chapter":"III","name":null,"page":34,"title":"Zweite Ableitung längs Kurven","note":null,"deps":["2:III.12","2:II.11","2:II.8"],"links":["2:III.12","2:II.11","2:II.8"],"implied":[],"depth":25,"weight":4,"pos":[4192,5390.7,9],"landmark":false,"img":{"s":[983,93],"p":[983,511]}},{"id":"2:V.11","label":"V.11","course":"2","kind":"Definition","chapter":"V","name":null,"page":83,"title":"Gradientenfeld (konservatives Feld)","note":null,"deps":["2:II.9"],"links":["2:II.9"],"implied":[],"depth":25,"weight":10,"pos":[4913.5,5505.4,10.7],"landmark":false,"img":{"s":[983,99]}},{"id":"3:VII.4","label":"VII.4","course":"3","kind":"Satz","chapter":"VII","name":null,"page":95,"title":"Gradient und Laplace in krummlinigen Koordinaten","note":null,"deps":["3:VII.1","2:II.11","2:II.9"],"links":["3:VII.1","2:II.11","2:II.9"],"implied":[],"depth":25,"weight":0,"pos":[4153.4,8127.6,6],"landmark":false,"img":{"s":[983,510],"p":[983,1825]}},{"id":"2:II.15","label":"II.15","course":"2","kind":"Korollar","chapter":"II","name":null,"page":26,"title":"Rechenregeln für Cᵏ-Funktionen","note":null,"deps":["2:II.2","2:II.14","2:II.11","2:II.3","1:II.3"],"links":["2:II.14","2:II.11","2:II.3"],"implied":[{"id":"2:II.2","via":"2:II.14"},{"id":"1:II.3","via":"2:II.2"}],"depth":25,"weight":61,"pos":[3344.9,5373.1,17.7],"landmark":false,"img":{"s":[983,1752]}},{"id":"2:V.28","label":"V.28","course":"2","kind":"Satz","chapter":"V","name":"Cauchy-Riemannsche Differentialgleichungen","page":94,"title":"Cauchy-Riemann-Gleichungen","note":null,"deps":["2:V.27","2:II.7","2:II.14"],"links":["2:V.27","2:II.14"],"implied":[{"id":"2:II.7","via":"2:II.14"}],"depth":25,"weight":6,"pos":[4963.6,5490.1,9.7],"landmark":false,"img":{"s":[983,299],"p":[983,1063]}},{"id":"L:19.9","label":"19.9","course":"L","kind":"Satz","chapter":"19","name":"Spektralsatz","page":222,"title":"Spektralsatz","note":null,"deps":["L:19.8","L:18.36","1:II.3"],"links":["L:19.8","L:18.36"],"implied":[{"id":"1:II.3","via":"L:19.8"}],"depth":25,"weight":32,"pos":[7126.4,3101.4,14.5],"landmark":true,"img":{"s":[983,340],"p":[983,652]}},{"id":"L:19.27","label":"19.27","course":"L","kind":"Satz","chapter":"19","name":null,"page":233,"title":"∣det Φ∣ = 1, Eigenwerte vom Betrag 1","note":null,"deps":["L:19.23","L:18.52","L:13.1"],"links":["L:19.23","L:18.52","L:13.1"],"implied":[],"depth":25,"weight":4,"pos":[7105.2,2860.7,9],"landmark":false,"img":{"s":[983,126],"p":[983,763]}},{"id":"L:16.4","label":"16.4","course":"L","kind":"Satz","chapter":"16","name":"Cayley-Hamilton","page":164,"title":"Satz von Cayley-Hamilton","note":null,"deps":["L:16.1","L:15.3","L:13.7"],"links":["L:16.1","L:15.3"],"implied":[{"id":"L:13.7","via":"L:15.3"}],"depth":25,"weight":1,"pos":[5864.2,3390.1,7.5],"landmark":true,"img":{"s":[983,105],"p":[983,2276]}},{"id":"L:17.12","label":"17.12","course":"L","kind":"Satz","chapter":"17","name":null,"page":177,"title":"Existenz der Jordanschen Normalform","note":null,"deps":["L:17.8","L:17.11","L:17.1"],"links":["L:17.8","L:17.11"],"implied":[{"id":"L:17.1","via":"L:17.11"}],"depth":25,"weight":6,"pos":[6308.9,3234.2,9.7],"landmark":true,"img":{"s":[983,163]}},{"id":"1:VII.12","label":"VII.12","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":88,"title":"Differenzformeln für sin und cos","note":null,"deps":["1:V.19"],"links":["1:V.19"],"implied":[],"depth":26,"weight":8,"pos":[1212.5,3859.9,10.2],"landmark":false,"img":{"s":[983,185],"p":[983,466]}},{"id":"1:VII.13","label":"VII.13","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":88,"title":"Abschätzungen für cos und sin auf [0,2]","note":null,"deps":["1:V.20","1:V.3"],"links":["1:V.20","1:V.3"],"implied":[],"depth":26,"weight":8,"pos":[1160.9,3850.1,10.2],"landmark":false,"img":{"s":[983,262],"p":[983,1061]}},{"id":"1:VII.10","label":"VII.10","course":"1","kind":"Definition","chapter":"VII","name":null,"page":86,"title":"Allgemeine Potenz aˣ und x^α","note":null,"deps":["1:VII.9"],"links":["1:VII.9"],"implied":[],"depth":26,"weight":9,"pos":[1270.1,3863.8,10.5],"landmark":false,"img":{"s":[983,384]}},{"id":"3:II.14","label":"II.14","course":"3","kind":"Lemma","chapter":"II","name":null,"page":24,"title":"Jede Fortsetzung liegt unter der Carathéodory-Fortsetzung","note":null,"deps":["3:II.13","3:I.3","3:I.7"],"links":["3:II.13","3:I.3"],"implied":[{"id":"3:I.7","via":"3:II.13"}],"depth":26,"weight":44,"pos":[4351.2,7828.5,15.9],"landmark":false,"img":{"s":[983,95],"p":[983,370]}},{"id":"3:II.16","label":"II.16","course":"3","kind":"Satz","chapter":"II","name":"Regularität der Caratheodory-Fortsetzung","page":25,"title":"Regularität der Carathéodory-Fortsetzung","note":null,"deps":["3:II.13","3:I.3"],"links":["3:II.13","3:I.3"],"implied":[],"depth":26,"weight":43,"pos":[4421.1,7843.2,15.8],"landmark":false,"img":{"s":[983,188],"p":[983,553]}},{"id":"3:IV.4","label":"IV.4","course":"3","kind":"Lemma","chapter":"IV","name":null,"page":49,"title":"Integral von Treppenfunktionen stimmt überein","note":null,"deps":["3:IV.2","3:IV.3"],"links":["3:IV.3"],"implied":[{"id":"3:IV.2","via":"3:IV.3"}],"depth":26,"weight":0,"pos":[2529.4,8107.4,6],"landmark":false,"img":{"s":[983,42],"p":[983,392]}},{"id":"3:IV.5","label":"IV.5","course":"3","kind":"Definition","chapter":"IV","name":null,"page":49,"title":"Integrierbare Funktion","note":null,"deps":["3:IV.3"],"links":["3:IV.3"],"implied":[],"depth":26,"weight":32,"pos":[2483.5,8132.9,14.5],"landmark":false,"img":{"s":[983,1521]}},{"id":"3:IV.6","label":"IV.6","course":"3","kind":"Satz","chapter":"IV","name":null,"page":50,"title":"Monotonie des Integrals","note":null,"deps":["3:IV.3","3:IV.2","3:I.8"],"links":["3:IV.3"],"implied":[{"id":"3:IV.2","via":"3:IV.3"},{"id":"3:I.8","via":"3:IV.3"}],"depth":26,"weight":45,"pos":[2617.6,8123.2,16.1],"landmark":false,"img":{"s":[983,389],"p":[983,1169]}},{"id":"3:IV.12","label":"IV.12","course":"3","kind":"Definition","chapter":"IV","name":null,"page":56,"title":"Integral über eine messbare Teilmenge","note":null,"deps":["3:IV.3","3:I.17"],"links":["3:IV.3","3:I.17"],"implied":[],"depth":26,"weight":15,"pos":[2561.9,8145.2,11.8],"landmark":false,"img":{"s":[983,1451]}},{"id":"3:V.7","label":"V.7","course":"3","kind":"Definition","chapter":"V","name":"L p -Norm","page":64,"title":"Lᵖ-Norm","note":null,"deps":["3:IV.3","3:I.18"],"links":["3:IV.3"],"implied":[{"id":"3:I.18","via":"3:IV.3"}],"depth":26,"weight":19,"pos":[4672.8,8460.5,12.5],"landmark":false,"img":{"s":[983,290]}},{"id":"2:V.26","label":"V.26","course":"2","kind":"Satz","chapter":"V","name":null,"page":93,"title":"Pullback von 1-Formen","note":null,"deps":["2:V.24","2:II.11"],"links":["2:V.24","2:II.11"],"implied":[],"depth":26,"weight":0,"pos":[4916,5390.5,6],"landmark":false,"img":{"s":[983,158],"p":[983,839]}},{"id":"2:V.18","label":"V.18","course":"2","kind":"Satz","chapter":"V","name":"Fundamentalsatz der Algebra","page":87,"title":"Fundamentalsatz der Algebra (Beweis)","note":"Liefert den in Ana I (Satz IV.28) ausstehenden Beweis","deps":["2:V.17","2:V.8","1:IV.23"],"links":["2:V.17","1:IV.23"],"implied":[{"id":"2:V.8","via":"2:V.17"}],"depth":26,"weight":0,"pos":[5005.2,5616.3,6],"landmark":false,"img":{"s":[983,70],"p":[983,1212]}},{"id":"2:V.19","label":"V.19","course":"2","kind":"Lemma","chapter":"V","name":null,"page":88,"title":"Homotopieinvarianz für nahe Kurven","note":null,"deps":["2:V.17","2:V.16"],"links":["2:V.17"],"implied":[{"id":"2:V.16","via":"2:V.17"}],"depth":26,"weight":8,"pos":[5053.4,5615,10.2],"landmark":false,"img":{"s":[983,262],"p":[983,98]}},{"id":"1:IX.6","label":"IX.6","course":"1","kind":"Satz","chapter":"IX","name":"Vertauschung von Konvergenz und Ableitung","page":113,"title":"Vertauschung von Grenzwert und Ableitung","note":null,"deps":["1:IX.2","1:IX.3","1:VIII.17","1:VIII.19","1:VIII.2"],"links":["1:IX.2","1:IX.3","1:VIII.17","1:VIII.19"],"implied":[{"id":"1:VIII.2","via":"1:VIII.17"}],"depth":26,"weight":10,"pos":[2991,3583.4,10.7],"landmark":true,"img":{"s":[983,253],"p":[983,1118]}},{"id":"1:XI.5","label":"XI.5","course":"1","kind":"Lemma","chapter":"XI","name":null,"page":129,"title":"∫ₐᵇ f = F(b) − F(a)","note":null,"deps":["1:XI.4"],"links":["1:XI.4"],"implied":[],"depth":26,"weight":78,"pos":[3814.8,3836.8,19.2],"landmark":false,"img":{"s":[983,133],"p":[983,166]}},{"id":"2:V.15","label":"V.15","course":"2","kind":"Satz","chapter":"V","name":null,"page":85,"title":"Integrabilitätsbedingung ∂ᵢFⱼ = ∂ⱼFᵢ","note":null,"deps":["2:V.11","2:II.4"],"links":["2:V.11","2:II.4"],"implied":[],"depth":26,"weight":7,"pos":[4932.6,5559.9,10],"landmark":false,"img":{"s":[983,140],"p":[983,1246]}},{"id":"2:IV.3","label":"IV.3","course":"2","kind":"Lemma","chapter":"IV","name":null,"page":61,"title":"Umkehrabbildung ist Cʳ","note":null,"deps":["2:IV.2","2:II.15","L:12.20","L:12.17"],"links":["2:IV.2","2:II.15","L:12.20"],"implied":[{"id":"L:12.17","via":"L:12.20"}],"depth":26,"weight":25,"pos":[3070.9,5810.7,13.5],"landmark":false,"img":{"s":[983,99],"p":[983,578]}},{"id":"L:19.10","label":"19.10","course":"L","kind":"Korollar","chapter":"19","name":"Spektralsatz für Matrizen","page":223,"title":"Spektralsatz für Matrizen","note":null,"deps":["L:19.9","L:18.49"],"links":["L:19.9","L:18.49"],"implied":[],"depth":26,"weight":18,"pos":[7151.1,3154.8,12.4],"landmark":false,"img":{"s":[983,285],"p":[983,104]}},{"id":"L:20.15","label":"20.15","course":"L","kind":"Satz","chapter":"20","name":"Hauptachsen-Transformation","page":248,"title":"Hauptachsentransformation","note":null,"deps":["L:20.9","L:19.9"],"links":["L:20.9","L:19.9"],"implied":[],"depth":26,"weight":15,"pos":[6915.9,3313.9,11.8],"landmark":true,"img":{"s":[983,195],"p":[983,757]}},{"id":"L:19.28","label":"19.28","course":"L","kind":"Satz","chapter":"19","name":"Diagonalisierbarkeit","page":234,"title":"Unitäre Isometrien sind diagonalisierbar","note":null,"deps":["L:19.27","L:18.36","L:13.8"],"links":["L:19.27","L:18.36","L:13.8"],"implied":[],"depth":26,"weight":3,"pos":[7107.4,2915.2,8.6],"landmark":false,"img":{"s":[983,99],"p":[983,495]}},{"id":"L:16.6","label":"16.6","course":"L","kind":"Korollar","chapter":"16","name":null,"page":165,"title":"Cayley-Hamilton für Matrizen","note":null,"deps":["L:16.4","L:10.2"],"links":["L:16.4"],"implied":[{"id":"L:10.2","via":"L:16.4"}],"depth":26,"weight":0,"pos":[5857.6,3463.8,6],"landmark":false,"img":{"s":[983,36],"p":[983,1517]}},{"id":"L:17.13","label":"17.13","course":"L","kind":"Korollar","chapter":"17","name":"Jordansche Normalform einer komplexen Matrix","page":177,"title":"Jordansche Normalform komplexer Matrizen","note":null,"deps":["L:17.12","L:10.9"],"links":["L:17.12","L:10.9"],"implied":[],"depth":26,"weight":2,"pos":[6233.8,3300.4,8.1],"landmark":false,"img":{"s":[983,227],"p":[983,375]}},{"id":"L:17.15","label":"17.15","course":"L","kind":"Satz","chapter":"17","name":null,"page":184,"title":"Anzahl der Kästchen = Dimension des Eigenraums","note":null,"deps":["L:17.12"],"links":["L:17.12"],"implied":[],"depth":26,"weight":0,"pos":[6301,3313.9,6],"landmark":false,"img":{"s":[983,72],"p":[983,308]}},{"id":"L:17.16","label":"17.16","course":"L","kind":"Satz","chapter":"17","name":null,"page":184,"title":"Anzahl der Kästchen gegebener Größe","note":null,"deps":["L:17.12","L:9.21"],"links":["L:17.12"],"implied":[{"id":"L:9.21","via":"L:17.12"}],"depth":26,"weight":0,"pos":[6270.5,3272.5,6],"landmark":false,"img":{"s":[983,169],"p":[983,517]}},{"id":"1:VII.14","label":"VII.14","course":"1","kind":"Satz","chapter":"VII","name":null,"page":89,"title":"Definition von π","note":null,"deps":["1:VII.13","1:VII.1","1:VII.12","1:V.19","1:V.18"],"links":["1:VII.13","1:VII.1","1:VII.12"],"implied":[{"id":"1:V.19","via":"1:VII.12"},{"id":"1:V.18","via":"1:VII.13"}],"depth":27,"weight":7,"pos":[1195.4,3914,10],"landmark":true,"img":{"s":[983,196],"p":[983,715]}},{"id":"1:VII.11","label":"VII.11","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":86,"title":"Funktionalgleichung der Exponentialfunktion","note":null,"deps":["1:VII.10","1:VI.3","1:I.20","1:III.15"],"links":["1:VII.10","1:I.20"],"implied":[{"id":"1:VI.3","via":"1:VII.10"},{"id":"1:III.15","via":"1:VII.10"}],"depth":27,"weight":0,"pos":[1310.7,3837.3,6],"landmark":false,"img":{"s":[983,226],"p":[983,1567]}},{"id":"1:VIII.9","label":"VIII.9","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":98,"title":"Ableitung von aˣ, sin, cos","note":null,"deps":["1:V.exp","1:V.17","1:V.18","1:VII.10","1:VIII.7","1:VIII.2"],"links":["1:V.18","1:VII.10","1:VIII.7","1:VIII.2"],"implied":[{"id":"1:V.exp","via":"1:V.17"},{"id":"1:V.17","via":"1:V.18"}],"depth":27,"weight":7,"pos":[2085.7,3733.3,10],"landmark":false,"img":{"s":[983,113],"p":[983,884]}},{"id":"3:II.15","label":"II.15","course":"3","kind":"Satz","chapter":"II","name":null,"page":24,"title":"Existenz und Eindeutigkeit der Fortsetzung","note":null,"deps":["3:II.13","3:II.7","3:I.7","3:II.14","3:I.6"],"links":["3:II.14","3:I.6"],"implied":[{"id":"3:II.13","via":"3:II.14"},{"id":"3:II.7","via":"3:II.13"},{"id":"3:I.7","via":"3:II.13"}],"depth":27,"weight":43,"pos":[4355.8,7898.2,15.8],"landmark":false,"img":{"s":[983,95],"p":[983,897]}},{"id":"3:IV.7","label":"IV.7","course":"3","kind":"Lemma","chapter":"IV","name":"Tschebyscheff-Ungleichung","page":52,"title":"Tschebyscheff-Ungleichung","note":null,"deps":["3:IV.3","3:IV.6"],"links":["3:IV.6"],"implied":[{"id":"3:IV.3","via":"3:IV.6"}],"depth":27,"weight":34,"pos":[2620.4,8208,14.7],"landmark":false,"img":{"s":[983,134],"p":[983,105]}},{"id":"3:IV.10","label":"IV.10","course":"3","kind":"Satz","chapter":"IV","name":"Monotone Konvergenz, Satz von Beppo-Levi","page":53,"title":"Satz von der monotonen Konvergenz (Beppo Levi)","note":null,"deps":["3:IV.9","3:IV.6","3:IV.2","3:I.16","3:I.7"],"links":["3:IV.9","3:IV.6","3:I.7"],"implied":[{"id":"3:IV.2","via":"3:IV.6"},{"id":"3:I.16","via":"3:IV.9"}],"depth":27,"weight":39,"pos":[2698.8,8210.5,15.4],"landmark":true,"img":{"s":[983,145],"p":[983,925]}},{"id":"3:VIII.2","label":"VIII.2","course":"3","kind":"Definition","chapter":"VIII","name":"Flächenformel","page":97,"title":"Flächeninhalt einer Immersion","note":null,"deps":["3:VIII.1","3:IV.12"],"links":["3:VIII.1","3:IV.12"],"implied":[],"depth":27,"weight":9,"pos":[4949.1,8507.2,10.5],"landmark":false,"img":{"s":[983,2410]}},{"id":"3:X.6","label":"X.6","course":"3","kind":"Definition","chapter":"X","name":null,"page":122,"title":"Fourier-Transformation","note":null,"deps":["3:IV.12","1:V.18"],"links":["3:IV.12","1:V.18"],"implied":[],"depth":27,"weight":4,"pos":[3961.5,9168.1,9],"landmark":false,"img":{"s":[983,399]}},{"id":"3:V.8","label":"V.8","course":"3","kind":"Definition","chapter":"V","name":null,"page":64,"title":"Lᵖ(E) auf Teilmengen","note":null,"deps":["3:V.7"],"links":["3:V.7"],"implied":[],"depth":27,"weight":0,"pos":[4790.6,8532,6],"landmark":false,"img":{"s":[983,315]}},{"id":"3:V.11","label":"V.11","course":"3","kind":"Satz","chapter":"V","name":"Höldersche Ungleichung","page":66,"title":"Höldersche Ungleichung","note":null,"deps":["3:V.10","3:IV.6","3:V.7"],"links":["3:V.10","3:IV.6","3:V.7"],"implied":[],"depth":27,"weight":17,"pos":[4697.4,8541.9,12.2],"landmark":true,"img":{"s":[983,166],"p":[983,228]}},{"id":"2:V.20","label":"V.20","course":"2","kind":"Satz","chapter":"V","name":"Homotopieinvarianz des Kurvenintegrals","page":88,"title":"Homotopieinvarianz des Kurvenintegrals","note":null,"deps":["2:V.19","2:V.17","2:I.23","2:I.21"],"links":["2:V.19","2:I.21"],"implied":[{"id":"2:V.17","via":"2:V.19"},{"id":"2:I.23","via":"2:V.19"}],"depth":27,"weight":7,"pos":[4885.9,5663.6,10],"landmark":true,"img":{"s":[983,185],"p":[983,1816]}},{"id":"1:IX.7","label":"IX.7","course":"1","kind":"Satz","chapter":"IX","name":null,"page":114,"title":"Potenzreihen gliedweise ableiten","note":null,"deps":["1:IX.6","1:IX.5","1:V.10"],"links":["1:IX.6","1:IX.5"],"implied":[{"id":"1:V.10","via":"1:IX.5"}],"depth":27,"weight":9,"pos":[2955.2,3659.4,10.5],"landmark":false,"img":{"s":[983,317],"p":[983,2995]}},{"id":"1:XI.6","label":"XI.6","course":"1","kind":"Satz","chapter":"XI","name":"Partielle Integration","page":129,"title":"Partielle Integration","note":null,"deps":["1:VIII.6","1:XI.5","1:X.11"],"links":["1:XI.5"],"implied":[{"id":"1:VIII.6","via":"1:XI.5"},{"id":"1:X.11","via":"1:XI.5"}],"depth":27,"weight":14,"pos":[3715.9,3872.3,11.6],"landmark":true,"img":{"s":[983,127],"p":[983,126]}},{"id":"1:XI.7","label":"XI.7","course":"1","kind":"Satz","chapter":"XI","name":"Substitutionsformel","page":129,"title":"Substitutionsregel","note":null,"deps":["1:XI.3","1:XI.5","1:VIII.7"],"links":["1:XI.5","1:VIII.7"],"implied":[{"id":"1:XI.3","via":"1:XI.5"}],"depth":27,"weight":6,"pos":[3767.5,3885.5,9.7],"landmark":true,"img":{"s":[983,166],"p":[983,4735]}},{"id":"2:III.1","label":"III.1","course":"2","kind":"Lemma","chapter":"III","name":null,"page":29,"title":"Hauptsatz längs Kurven","note":null,"deps":["2:II.15","2:II.11","1:XI.5"],"links":["2:II.15","1:XI.5"],"implied":[{"id":"2:II.11","via":"2:II.15"}],"depth":27,"weight":59,"pos":[4107.6,5471.7,17.5],"landmark":false,"img":{"s":[983,149],"p":[983,423]}},{"id":"L:19.13","label":"19.13","course":"L","kind":"Satz","chapter":"19","name":"Ein Kriterium für “positiv definit”","page":225,"title":"Positiv definit ⇔ alle Eigenwerte positiv","note":null,"deps":["L:19.10","L:18.8"],"links":["L:19.10","L:18.8"],"implied":[],"depth":27,"weight":17,"pos":[7137.5,3218,12.2],"landmark":false,"img":{"s":[983,132],"p":[983,630]}},{"id":"L:20.17","label":"20.17","course":"L","kind":"Satz","chapter":"20","name":"Trägheitssatz von Sylvester","page":250,"title":"Trägheitssatz von Sylvester","note":null,"deps":["L:20.15","L:20.14","L:20.8"],"links":["L:20.15","L:20.14","L:20.8"],"implied":[],"depth":27,"weight":8,"pos":[6898.8,3367.9,10.2],"landmark":true,"img":{"s":[983,317],"p":[983,1013]}},{"id":"L:20.26","label":"20.26","course":"L","kind":"Satz","chapter":"20","name":null,"page":257,"title":"Extremaleigenschaft der Eigenwerte","note":null,"deps":["L:20.15"],"links":["L:20.15"],"implied":[],"depth":27,"weight":0,"pos":[6942.3,3388.7,6],"landmark":false,"img":{"s":[983,166],"p":[983,1613]}},{"id":"L:20.27","label":"20.27","course":"L","kind":"Definition","chapter":"20","name":null,"page":258,"title":"Übersicht: Äquivalenz, Ähnlichkeit, Kongruenz","note":null,"deps":["L:17.12","L:20.15","L:10.7","L:10.9"],"links":["L:17.12","L:20.15","L:10.7","L:10.9"],"implied":[],"depth":27,"weight":0,"pos":[6814.4,3358.1,6],"landmark":false,"img":{"s":[983,2044]}},{"id":"L:21.43","label":"21.43","course":"L","kind":"Satz","chapter":"21","name":null,"page":281,"title":"Euklidische Normalformen von Quadriken im ℝ³","note":null,"deps":["L:21.38","L:20.15","L:21.35"],"links":["L:21.38","L:20.15","L:21.35"],"implied":[],"depth":27,"weight":2,"pos":[7132.1,2619.3,8.1],"landmark":false,"img":{"s":[983,1186]}},{"id":"L:19.30","label":"19.30","course":"L","kind":"Korollar","chapter":"19","name":"Unitäre Normalform ist diagonal","page":235,"title":"Unitäre Normalform","note":null,"deps":["L:19.28","L:18.49"],"links":["L:19.28"],"implied":[{"id":"L:18.49","via":"L:19.28"}],"depth":27,"weight":0,"pos":[7126.2,2978,6],"landmark":false,"img":{"s":[983,332],"p":[983,766]}},{"id":"L:19.31","label":"19.31","course":"L","kind":"Satz","chapter":"19","name":"euklidische Normalform: Dreh-Kästchen","page":236,"title":"Euklidische Normalform: Drehkästchen","note":null,"deps":["L:19.28","L:19.27"],"links":["L:19.28"],"implied":[{"id":"L:19.27","via":"L:19.28"}],"depth":27,"weight":1,"pos":[7167.4,2997.4,7.5],"landmark":false,"img":{"s":[983,681]}},{"id":"1:VII.15","label":"VII.15","course":"1","kind":"Lemma","chapter":"VII","name":null,"page":90,"title":"Verschiebung um π/2","note":null,"deps":["1:VII.14","1:V.17","1:V.18"],"links":["1:VII.14"],"implied":[{"id":"1:V.17","via":"1:VII.14"},{"id":"1:V.18","via":"1:VII.14"}],"depth":28,"weight":6,"pos":[1179.9,3975.2,9.7],"landmark":false,"img":{"s":[983,122],"p":[983,965]}},{"id":"1:VIII.10","label":"VIII.10","course":"1","kind":"Satz","chapter":"VIII","name":null,"page":99,"title":"Ableitung von log","note":null,"deps":["1:VIII.8","1:VIII.9","1:VII.9"],"links":["1:VIII.8","1:VIII.9"],"implied":[{"id":"1:VII.9","via":"1:VIII.9"}],"depth":28,"weight":0,"pos":[2196.5,3800.9,6],"landmark":false,"img":{"s":[983,81],"p":[983,122]}},{"id":"1:VIII.15","label":"VIII.15","course":"1","kind":"Lemma","chapter":"VIII","name":null,"page":101,"title":"y′ = ay hat nur Lösungen ce^{ax}","note":null,"deps":["1:VIII.14","1:VIII.9","1:VIII.6","1:VIII.7"],"links":["1:VIII.14","1:VIII.9"],"implied":[{"id":"1:VIII.6","via":"1:VIII.14"},{"id":"1:VIII.7","via":"1:VIII.9"}],"depth":28,"weight":5,"pos":[2244.3,3789.3,9.4],"landmark":false,"img":{"s":[983,152],"p":[983,206]}},{"id":"3:II.17","label":"II.17","course":"3","kind":"Satz","chapter":"II","name":null,"page":26,"title":"M(µ) ist die Vervollständigung von σ(R)","note":null,"deps":["3:II.7","3:I.10","3:II.16","3:II.15"],"links":["3:I.10","3:II.16","3:II.15"],"implied":[{"id":"3:II.7","via":"3:II.16"}],"depth":28,"weight":42,"pos":[4402.6,7960,15.7],"landmark":false,"img":{"s":[983,163],"p":[983,803]}},{"id":"3:IV.8","label":"IV.8","course":"3","kind":"Lemma","chapter":"IV","name":null,"page":52,"title":"Endliches Integral ⇒ f fast überall endlich","note":null,"deps":["3:IV.7","3:II.8"],"links":["3:IV.7","3:II.8"],"implied":[],"depth":28,"weight":33,"pos":[2665.5,8262.8,14.6],"landmark":false,"img":{"s":[983,188],"p":[983,107]}},{"id":"3:V.1","label":"V.1","course":"3","kind":"Satz","chapter":"V","name":"Lemma von Fatou","page":59,"title":"Lemma von Fatou","note":null,"deps":["3:IV.10","3:I.16"],"links":["3:IV.10"],"implied":[{"id":"3:I.16","via":"3:IV.10"}],"depth":28,"weight":30,"pos":[4636.2,8572.7,14.2],"landmark":true,"img":{"s":[983,140],"p":[983,188]}},{"id":"3:VI.3","label":"VI.3","course":"3","kind":"Lemma","chapter":"VI","name":null,"page":76,"title":"Produktmengen sind messbar mit µ(A×B) = α(A)β(B)","note":null,"deps":["3:VI.1","3:VI.2","3:IV.10"],"links":["3:VI.2","3:IV.10"],"implied":[{"id":"3:VI.1","via":"3:VI.2"}],"depth":28,"weight":17,"pos":[3324.5,8473.3,12.2],"landmark":false,"img":{"s":[983,169],"p":[983,1411]}},{"id":"3:V.12","label":"V.12","course":"3","kind":"Satz","chapter":"V","name":"Minkowski-Ungleichung","page":66,"title":"Minkowski-Ungleichung","note":null,"deps":["3:V.11","3:V.7"],"links":["3:V.11"],"implied":[{"id":"3:V.7","via":"3:V.11"}],"depth":28,"weight":16,"pos":[4765.6,8613.6,12],"landmark":false,"img":{"s":[983,94],"p":[983,204]}},{"id":"2:V.30","label":"V.30","course":"2","kind":"Satz","chapter":"V","name":"Cauchy Integralsatz","page":96,"title":"Cauchyscher Integralsatz","note":null,"deps":["2:V.29","2:V.28","2:V.20","2:V.15"],"links":["2:V.29","2:V.28","2:V.20","2:V.15"],"implied":[],"depth":28,"weight":4,"pos":[4992.9,5725.7,9],"landmark":true,"img":{"s":[983,182],"p":[983,587]}},{"id":"2:III.14","label":"III.14","course":"2","kind":"Lemma","chapter":"III","name":null,"page":35,"title":"Entwicklung zweiter Ordnung","note":null,"deps":["2:III.13","1:XI.6"],"links":["2:III.13","1:XI.6"],"implied":[],"depth":28,"weight":3,"pos":[4242.8,5476.6,8.6],"landmark":false,"img":{"s":[983,121],"p":[983,1004]}},{"id":"2:III.22","label":"III.22","course":"2","kind":"Satz","chapter":"III","name":"Integraldarstellung des Restglieds","page":41,"title":"Integraldarstellung des Restglieds","note":null,"deps":["2:III.21","1:XI.5","1:XI.6","1:II.3"],"links":["2:III.21","1:XI.6"],"implied":[{"id":"1:XI.5","via":"1:XI.6"},{"id":"1:II.3","via":"2:III.21"}],"depth":28,"weight":8,"pos":[4219.9,5058.1,10.2],"landmark":false,"img":{"s":[983,338],"p":[983,579]}},{"id":"2:III.36","label":"III.36","course":"2","kind":"Satz","chapter":"III","name":"Euler-Lagrange Gleichung","page":56,"title":"Euler-Lagrange-Gleichung","note":null,"deps":["2:III.34","2:III.35","1:XI.6"],"links":["2:III.34","2:III.35","1:XI.6"],"implied":[],"depth":28,"weight":0,"pos":[4095.9,5526,6],"landmark":false,"img":{"s":[983,355],"p":[983,1917]}},{"id":"2:V.4","label":"V.4","course":"2","kind":"Lemma","chapter":"V","name":"Invarianz der Bogenlänge","page":78,"title":"Invarianz der Bogenlänge","note":null,"deps":["2:V.2","2:V.3","1:XI.7"],"links":["2:V.2","2:V.3","1:XI.7"],"implied":[],"depth":28,"weight":0,"pos":[5015.1,5197.4,6],"landmark":false,"img":{"s":[983,70],"p":[983,629]}},{"id":"2:V.9","label":"V.9","course":"2","kind":"Lemma","chapter":"V","name":null,"page":81,"title":"Eigenschaften des Kurvenintegrals","note":null,"deps":["2:V.8","2:V.3","1:XI.7"],"links":["2:V.8","2:V.3","1:XI.7"],"implied":[],"depth":28,"weight":3,"pos":[5086.7,5333.7,8.6],"landmark":false,"img":{"s":[983,783],"p":[983,843]}},{"id":"2:VI.3","label":"VI.3","course":"2","kind":"Satz","chapter":"VI","name":null,"page":103,"title":"Trennung der Variablen","note":null,"deps":["2:VI.1","1:XI.3","1:XI.7","1:VII.7","1:VIII.8"],"links":["2:VI.1","1:XI.7","1:VIII.8"],"implied":[{"id":"1:XI.3","via":"1:XI.7"},{"id":"1:VII.7","via":"1:VIII.8"}],"depth":28,"weight":0,"pos":[4434.1,5488.9,6],"landmark":false,"img":{"s":[983,471],"p":[983,4142]}},{"id":"2:III.2","label":"III.2","course":"2","kind":"Satz","chapter":"III","name":null,"page":29,"title":"Df = 0 auf zusammenhängendem Ω ⇒ konstant","note":null,"deps":["2:III.1","2:I.25"],"links":["2:III.1","2:I.25"],"implied":[],"depth":28,"weight":1,"pos":[4122,5563.2,7.5],"landmark":false,"img":{"s":[983,93],"p":[983,325]}},{"id":"2:III.7","label":"III.7","course":"2","kind":"Satz","chapter":"III","name":"Schrankensatz","page":31,"title":"Schrankensatz","note":null,"deps":["2:III.6","2:III.1","1:IV.11"],"links":["2:III.6","2:III.1"],"implied":[{"id":"1:IV.11","via":"2:III.1"}],"depth":28,"weight":53,"pos":[4178.5,5563.3,16.9],"landmark":true,"img":{"s":[983,251],"p":[983,851]}},{"id":"L:19.15","label":"19.15","course":"L","kind":"Korollar","chapter":"19","name":"“Wurzel” aus einer positiv definiten Matrix","page":226,"title":"Wurzel einer positiv definiten Matrix","note":null,"deps":["L:19.10","L:19.13"],"links":["L:19.13"],"implied":[{"id":"L:19.10","via":"L:19.13"}],"depth":28,"weight":14,"pos":[7145,3289.8,11.6],"landmark":false,"img":{"s":[983,100],"p":[983,669]}},{"id":"L:20.21","label":"20.21","course":"L","kind":"Korollar","chapter":"20","name":"Simultanes Diagonalisieren von quadratischen Formen","page":252,"title":"Simultane Diagonalisierung","note":null,"deps":["L:20.15","L:19.13"],"links":["L:20.15","L:19.13"],"implied":[],"depth":28,"weight":0,"pos":[6896.4,3442.4,6],"landmark":false,"img":{"s":[983,236],"p":[983,470]}},{"id":"L:20.18","label":"20.18","course":"L","kind":"Definition","chapter":"20","name":null,"page":251,"title":"Signatur, Definitheit quadratischer Formen","note":null,"deps":["L:20.17"],"links":["L:20.17"],"implied":[],"depth":28,"weight":6,"pos":[6943.1,3452,9.7],"landmark":false,"img":{"s":[983,410]}},{"id":"L:21.45","label":"21.45","course":"L","kind":"Satz","chapter":"21","name":null,"page":284,"title":"Euklidische Klassifikation der Quadriken","note":null,"deps":["L:21.43"],"links":["L:21.43"],"implied":[],"depth":28,"weight":1,"pos":[7084.8,2690,7.5],"landmark":false,"img":{"s":[983,73],"p":[983,291]}},{"id":"L:19.34","label":"19.34","course":"L","kind":"Satz","chapter":"19","name":null,"page":239,"title":"Normalform orthogonaler Matrizen","note":null,"deps":["L:19.31","L:18.49"],"links":["L:19.31"],"implied":[{"id":"L:18.49","via":"L:19.31"}],"depth":28,"weight":0,"pos":[7143.4,3043.7,6],"landmark":false,"img":{"s":[983,1275]}},{"id":"1:VII.16","label":"VII.16","course":"1","kind":"Satz","chapter":"VII","name":null,"page":90,"title":"arccos und arcsin","note":null,"deps":["1:VII.7","1:VII.14","1:VII.15"],"links":["1:VII.7","1:VII.15"],"implied":[{"id":"1:VII.14","via":"1:VII.15"}],"depth":29,"weight":5,"pos":[1247.4,4033,9.4],"landmark":false,"img":{"s":[983,359],"p":[983,35]}},{"id":"3:II.18","label":"II.18","course":"3","kind":"Lemma","chapter":"II","name":null,"page":26,"title":"Charakterisierung µ-messbarer Mengen","note":null,"deps":["3:II.16","3:II.17"],"links":["3:II.17"],"implied":[{"id":"3:II.16","via":"3:II.17"}],"depth":29,"weight":41,"pos":[4415.4,8022.8,15.6],"landmark":false,"img":{"s":[983,352],"p":[983,168]}},{"id":"3:IV.11","label":"IV.11","course":"3","kind":"Satz","chapter":"IV","name":null,"page":54,"title":"Linearität des Integrals","note":null,"deps":["3:IV.2","3:IV.9","3:IV.10","3:IV.8","3:IV.5"],"links":["3:IV.10","3:IV.8","3:IV.5"],"implied":[{"id":"3:IV.2","via":"3:IV.10"},{"id":"3:IV.9","via":"3:IV.10"}],"depth":29,"weight":31,"pos":[2578,8308,14.4],"landmark":false,"img":{"s":[983,198],"p":[983,2680]}},{"id":"3:V.9","label":"V.9","course":"3","kind":"Proposition","chapter":"V","name":null,"page":65,"title":"Lᵖ ist ein normierter Raum","note":null,"deps":["3:V.7","3:V.12","3:IV.6","3:IV.8","2:I.2"],"links":["3:V.12","3:IV.8","2:I.2"],"implied":[{"id":"3:V.7","via":"3:V.12"},{"id":"3:IV.6","via":"3:V.12"}],"depth":29,"weight":2,"pos":[4662.4,8644.9,8.1],"landmark":false,"img":{"s":[983,197],"p":[983,395]}},{"id":"2:V.33","label":"V.33","course":"2","kind":"Satz","chapter":"V","name":"Cauchy-Integralformel","page":98,"title":"Cauchysche Integralformel","note":null,"deps":["2:V.30","2:V.10","2:V.17"],"links":["2:V.30","2:V.10"],"implied":[{"id":"2:V.17","via":"2:V.30"}],"depth":29,"weight":3,"pos":[4991.9,5787.9,8.6],"landmark":true,"img":{"s":[983,164],"p":[983,571]}},{"id":"2:III.23","label":"III.23","course":"2","kind":"Satz","chapter":"III","name":"Lagrangedarstellung des Restglieds","page":42,"title":"Lagrange-Restglied","note":null,"deps":["2:III.22","1:X.13"],"links":["2:III.22","1:X.13"],"implied":[],"depth":29,"weight":6,"pos":[4087.4,5118,9.7],"landmark":false,"img":{"s":[983,190],"p":[983,1759]}},{"id":"2:III.27","label":"III.27","course":"2","kind":"Lemma","chapter":"III","name":null,"page":45,"title":"Analytisch ⇔ Restglied → 0","note":null,"deps":["2:III.26","2:III.25","2:III.22","1:IX.7"],"links":["2:III.26","2:III.25","2:III.22","1:IX.7"],"implied":[],"depth":29,"weight":0,"pos":[4204.9,5119.8,6],"landmark":false,"img":{"s":[983,238],"p":[983,1632]}},{"id":"2:V.14","label":"V.14","course":"2","kind":"Satz","chapter":"V","name":null,"page":84,"title":"Gradientenfeld ⇔ wegunabhängige Kurvenintegrale","note":null,"deps":["2:V.9","2:V.11","2:V.13","2:III.1","2:III.4","2:II.14"],"links":["2:V.9","2:V.11","2:V.13","2:III.1","2:III.4"],"implied":[{"id":"2:II.14","via":"2:III.1"}],"depth":29,"weight":2,"pos":[4927.5,5611.8,8.1],"landmark":true,"img":{"s":[983,412],"p":[983,1558]}},{"id":"2:V.12","label":"V.12","course":"2","kind":"Lemma","chapter":"V","name":null,"page":83,"title":"Stammfunktion eindeutig bis auf Konstante","note":null,"deps":["2:V.11","2:III.2","2:III.5"],"links":["2:V.11","2:III.2","2:III.5"],"implied":[],"depth":29,"weight":0,"pos":[4952.9,5669.4,6],"landmark":false,"img":{"s":[983,95],"p":[983,275]}},{"id":"2:III.8","label":"III.8","course":"2","kind":"Lemma","chapter":"III","name":null,"page":32,"title":"Lokal Lipschitz auf Kompakta","note":null,"deps":["2:III.7","2:I.22","2:I.15"],"links":["2:III.7","2:I.22"],"implied":[{"id":"2:I.15","via":"2:I.22"}],"depth":29,"weight":37,"pos":[4121.7,5617.8,15.1],"landmark":false,"img":{"s":[983,122],"p":[983,973]}},{"id":"2:IV.6","label":"IV.6","course":"2","kind":"Satz","chapter":"IV","name":"Satz über inverse Funktionen","page":62,"title":"Satz über inverse Funktionen","note":null,"deps":["2:IV.5","2:IV.3","2:III.7","2:II.7","2:I.8","1:VI.6"],"links":["2:IV.5","2:IV.3","2:III.7","2:I.8"],"implied":[{"id":"2:II.7","via":"2:IV.3"},{"id":"1:VI.6","via":"2:IV.3"}],"depth":29,"weight":24,"pos":[3083.3,5909.1,13.3],"landmark":true,"img":{"s":[983,398],"p":[983,2765]}},{"id":"L:20.25","label":"20.25","course":"L","kind":"Satz","chapter":"20","name":"Cartan-Zerlegung","page":255,"title":"Cartan-Zerlegung","note":null,"deps":["L:20.15","L:20.9","L:19.15"],"links":["L:20.15","L:19.15"],"implied":[{"id":"L:20.9","via":"L:20.15"}],"depth":29,"weight":0,"pos":[6926.5,3506.2,6],"landmark":false,"img":{"s":[983,104],"p":[983,1919]}},{"id":"3:III.15","label":"III.15","course":"3","kind":"Lemma","chapter":"III","name":"Polarzerlegung","page":44,"title":"Polarzerlegung","note":null,"deps":["2:III.18","L:19.15","L:19.10"],"links":["2:III.18","L:19.15"],"implied":[{"id":"L:19.10","via":"L:19.15"}],"depth":29,"weight":12,"pos":[2735.1,8431.5,11.2],"landmark":false,"img":{"s":[983,121],"p":[983,528]}},{"id":"L:20.22","label":"20.22","course":"L","kind":"Satz","chapter":"20","name":"Jacobi-Hurwitz","page":253,"title":"Hurwitz-Kriterium (Hauptminoren)","note":null,"deps":["L:19.13","L:12.16","L:20.18"],"links":["L:19.13","L:20.18"],"implied":[{"id":"L:12.16","via":"L:19.13"}],"depth":29,"weight":0,"pos":[6881.2,3487.5,6],"landmark":false,"img":{"s":[983,382],"p":[983,1817]}},{"id":"2:III.16","label":"III.16","course":"2","kind":"Definition","chapter":"III","name":null,"page":36,"title":"Definitheit","note":null,"deps":["L:20.1","L:20.18"],"links":["L:20.18"],"implied":[{"id":"L:20.1","via":"L:20.18"}],"depth":29,"weight":4,"pos":[4097.1,5020.4,9],"landmark":false,"img":{"s":[983,369]}},{"id":"L:21.47","label":"21.47","course":"L","kind":"Satz","chapter":"21","name":null,"page":286,"title":"Affine Klassifikation der Quadriken","note":null,"deps":["L:21.45","L:20.17","L:21.42"],"links":["L:21.45","L:20.17","L:21.42"],"implied":[],"depth":29,"weight":0,"pos":[7132.9,2733.2,6],"landmark":false,"img":{"s":[983,917],"p":[983,414]}},{"id":"1:VII.17","label":"VII.17","course":"1","kind":"Satz","chapter":"VII","name":"Polarkoordinaten","page":91,"title":"Polarkoordinaten","note":null,"deps":["1:VII.16","1:VII.15","1:V.19","1:IV.22"],"links":["1:VII.16"],"implied":[{"id":"1:VII.15","via":"1:VII.16"},{"id":"1:V.19","via":"1:VII.16"},{"id":"1:IV.22","via":"1:VII.16"}],"depth":30,"weight":1,"pos":[1194.3,4074,7.5],"landmark":false,"img":{"s":[983,73],"p":[983,954]}},{"id":"L:18.23","label":"18.23","course":"L","kind":"Definition","chapter":"18","name":null,"page":199,"title":"Winkel zwischen Vektoren","note":null,"deps":["L:18.12","1:VII.16"],"links":["L:18.12","1:VII.16"],"implied":[],"depth":30,"weight":2,"pos":[7207,1829.6,8.1],"landmark":false,"img":{"s":[983,735]}},{"id":"3:II.31","label":"II.31","course":"3","kind":"Satz","chapter":"II","name":null,"page":33,"title":"Fortsetzung eines Prämaßes vom Halbring","note":null,"deps":["3:II.3","3:II.16","3:II.7","3:II.17","3:II.18","3:II.30","3:II.13"],"links":["3:II.18","3:II.30"],"implied":[{"id":"3:II.3","via":"3:II.16"},{"id":"3:II.16","via":"3:II.17"},{"id":"3:II.7","via":"3:II.16"},{"id":"3:II.17","via":"3:II.18"},{"id":"3:II.13","via":"3:II.16"}],"depth":30,"weight":40,"pos":[4376.7,8072.6,15.5],"landmark":false,"img":{"s":[983,202],"p":[983,155]}},{"id":"3:IV.13","label":"IV.13","course":"3","kind":"Satz","chapter":"IV","name":null,"page":57,"title":"f integrierbar ⇔ ∣f∣ integrierbar, Majorante","note":null,"deps":["3:IV.11","3:IV.6"],"links":["3:IV.11"],"implied":[{"id":"3:IV.6","via":"3:IV.11"}],"depth":30,"weight":30,"pos":[2601.8,8372.1,14.2],"landmark":false,"img":{"s":[983,193],"p":[983,2040]}},{"id":"2:V.34","label":"V.34","course":"2","kind":"Satz","chapter":"V","name":"Holomorph ⇒ Analytisch","page":98,"title":"Holomorph ⇒ analytisch","note":null,"deps":["2:V.33","2:V.28","2:V.10","1:V.10","1:IX.6","1:IX.7"],"links":["2:V.33","1:IX.7"],"implied":[{"id":"2:V.28","via":"2:V.33"},{"id":"2:V.10","via":"2:V.33"},{"id":"1:V.10","via":"1:IX.7"},{"id":"1:IX.6","via":"1:IX.7"}],"depth":30,"weight":2,"pos":[5012.4,5844.8,8.1],"landmark":false,"img":{"s":[983,244],"p":[983,1394]}},{"id":"2:III.24","label":"III.24","course":"2","kind":"Satz","chapter":"III","name":null,"page":43,"title":"f = Pₖ + o(∣x − x₀∣ᵏ)","note":null,"deps":["2:III.23","2:III.21"],"links":["2:III.23"],"implied":[{"id":"2:III.21","via":"2:III.23"}],"depth":30,"weight":1,"pos":[4120.5,5174.7,7.5],"landmark":false,"img":{"s":[983,348],"p":[983,558]}},{"id":"2:III.28","label":"III.28","course":"2","kind":"Lemma","chapter":"III","name":null,"page":46,"title":"Mehrdimensionale Taylorformel (k-Linearformen)","note":null,"deps":["2:III.23","2:II.4","2:II.11","2:II.8","1:II.3"],"links":["2:III.23","2:II.4","2:II.11","2:II.8"],"implied":[{"id":"1:II.3","via":"2:III.23"}],"depth":30,"weight":4,"pos":[4045.2,5369.1,9],"landmark":false,"img":{"s":[983,165],"p":[983,738]}},{"id":"2:V.22","label":"V.22","course":"2","kind":"Satz","chapter":"V","name":null,"page":90,"title":"Einfach zusammenhängend: geschlossen ⇔ Gradientenfeld","note":null,"deps":["2:V.21","2:V.20","2:V.14","2:V.15"],"links":["2:V.21","2:V.20","2:V.14","2:V.15"],"implied":[],"depth":30,"weight":1,"pos":[5041.3,5723.1,7.5],"landmark":false,"img":{"s":[983,263],"p":[983,1245]}},{"id":"2:VI.7","label":"VI.7","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":108,"title":"Stetige Dₓf ⇒ lokal Lipschitz in x","note":null,"deps":["2:III.7","2:III.8"],"links":["2:III.8"],"implied":[{"id":"2:III.7","via":"2:III.8"}],"depth":30,"weight":16,"pos":[4449.3,6039,12],"landmark":false,"img":{"s":[983,1844]}},{"id":"2:IV.7","label":"IV.7","course":"2","kind":"Lemma","chapter":"IV","name":null,"page":64,"title":"Lokal invertierbar ⇒ offene Abbildung","note":null,"deps":["2:IV.6","2:I.4"],"links":["2:IV.6"],"implied":[{"id":"2:I.4","via":"2:IV.6"}],"depth":30,"weight":2,"pos":[3027.2,5967.1,8.1],"landmark":false,"img":{"s":[983,178],"p":[983,2171]}},{"id":"2:IV.10","label":"IV.10","course":"2","kind":"Satz","chapter":"IV","name":"Satz über Implizite Funktionen","page":69,"title":"Satz über implizite Funktionen","note":null,"deps":["2:IV.6","L:5.55","L:12.17"],"links":["2:IV.6"],"implied":[{"id":"L:5.55","via":"2:IV.6"},{"id":"L:12.17","via":"2:IV.6"}],"depth":30,"weight":18,"pos":[3076.3,5985.6,12.4],"landmark":true,"img":{"s":[983,350],"p":[983,2869]}},{"id":"2:III.17","label":"III.17","course":"2","kind":"Satz","chapter":"III","name":null,"page":36,"title":"Hinreichende und notwendige Bedingungen für Extrema","note":null,"deps":["2:III.10","2:III.13","2:III.14","2:III.15","2:III.16","1:VIII.20"],"links":["2:III.10","2:III.14","2:III.15","2:III.16","1:VIII.20"],"implied":[{"id":"2:III.13","via":"2:III.14"}],"depth":30,"weight":2,"pos":[4141.6,5519.8,8.1],"landmark":true,"img":{"s":[983,286],"p":[983,923]}},{"id":"1:VII.18","label":"VII.18","course":"1","kind":"Satz","chapter":"VII","name":null,"page":92,"title":"Einheitswurzeln","note":null,"deps":["1:VII.17","1:IV.25","1:V.17"],"links":["1:VII.17","1:IV.25"],"implied":[{"id":"1:V.17","via":"1:VII.17"}],"depth":31,"weight":0,"pos":[1193.7,4133.1,6],"landmark":false,"img":{"s":[983,220],"p":[983,316]}},{"id":"L:18.24","label":"18.24","course":"L","kind":"Lemma","chapter":"18","name":"Eigenschaften der Winkelfunktion","page":199,"title":"Eigenschaften des Winkels","note":null,"deps":["L:18.23"],"links":["L:18.23"],"implied":[],"depth":31,"weight":0,"pos":[7081.8,1924.1,6],"landmark":false,"img":{"s":[983,341],"p":[983,1010]}},{"id":"L:19.21","label":"19.21","course":"L","kind":"Korollar","chapter":"19","name":null,"page":229,"title":"Lineare Isometrien sind winkeltreu","note":null,"deps":["L:19.20","L:18.23"],"links":["L:19.20","L:18.23"],"implied":[],"depth":31,"weight":0,"pos":[7150.8,2534.9,6],"landmark":false,"img":{"s":[983,102],"p":[983,249]}},{"id":"3:III.2","label":"III.2","course":"3","kind":"Definition","chapter":"III","name":null,"page":35,"title":"Lebesgue-Maß","note":null,"deps":["3:II.31","3:III.1"],"links":["3:II.31","3:III.1"],"implied":[],"depth":31,"weight":39,"pos":[2813.5,9057.1,15.4],"landmark":true,"img":{"s":[983,474]}},{"id":"3:V.2","label":"V.2","course":"3","kind":"Satz","chapter":"V","name":"Dominierte Konvergenz bzw. Satz von Lebesgue","page":59,"title":"Satz von der dominierten Konvergenz (Lebesgue)","note":null,"deps":["3:V.1","3:IV.13","3:IV.11"],"links":["3:V.1","3:IV.13"],"implied":[{"id":"3:IV.11","via":"3:IV.13"}],"depth":31,"weight":29,"pos":[4684,8761.7,14.1],"landmark":true,"img":{"s":[983,425],"p":[983,831]}},{"id":"2:V.35","label":"V.35","course":"2","kind":"Lemma","chapter":"V","name":null,"page":99,"title":"Cauchy-Abschätzung","note":null,"deps":["2:V.34","2:V.33","2:V.10"],"links":["2:V.34"],"implied":[{"id":"2:V.33","via":"2:V.34"},{"id":"2:V.10","via":"2:V.34"}],"depth":31,"weight":1,"pos":[5012.5,5905.3,7.5],"landmark":false,"img":{"s":[983,110],"p":[983,610]}},{"id":"2:III.29","label":"III.29","course":"2","kind":"Satz","chapter":"III","name":null,"page":47,"title":"Taylorformel mit Multiindizes","note":null,"deps":["2:III.28","2:II.5"],"links":["2:III.28","2:II.5"],"implied":[],"depth":31,"weight":3,"pos":[4144,5378,8.6],"landmark":true,"img":{"s":[983,155],"p":[983,1642]}},{"id":"2:V.32","label":"V.32","course":"2","kind":"Lemma","chapter":"V","name":null,"page":97,"title":"Holomorphe Stammfunktion auf einfach zusammenhängenden Gebieten","note":null,"deps":["2:V.31","2:V.22","2:V.28"],"links":["2:V.31","2:V.22","2:V.28"],"implied":[],"depth":31,"weight":0,"pos":[5038.4,5786,6],"landmark":false,"img":{"s":[983,183],"p":[983,797]}},{"id":"2:VI.6","label":"VI.6","course":"2","kind":"Satz","chapter":"VI","name":null,"page":108,"title":"Eindeutigkeit von Lösungen","note":null,"deps":["2:VI.7","2:VI.1","2:I.26"],"links":["2:VI.7","2:VI.1","2:I.26"],"implied":[],"depth":31,"weight":13,"pos":[4402,6096.5,11.4],"landmark":false,"img":{"s":[983,246]}},{"id":"2:VI.10","label":"VI.10","course":"2","kind":"Satz","chapter":"VI","name":"Kurzzeitexistenzsatz von Picard-Lindelöf","page":110,"title":"Satz von Picard-Lindelöf","note":null,"deps":["2:IV.5","2:VI.8","2:VI.9","2:VI.7"],"links":["2:IV.5","2:VI.8","2:VI.9","2:VI.7"],"implied":[],"depth":31,"weight":13,"pos":[4456.6,6100.6,11.4],"landmark":true,"img":{"s":[983,381],"p":[983,2255]}},{"id":"2:IV.8","label":"IV.8","course":"2","kind":"Satz","chapter":"IV","name":null,"page":66,"title":"Legendre-Transformation","note":null,"deps":["2:IV.6","2:IV.7","2:III.16","2:II.11"],"links":["2:IV.7","2:III.16"],"implied":[{"id":"2:IV.6","via":"2:IV.7"},{"id":"2:II.11","via":"2:IV.6"}],"depth":31,"weight":1,"pos":[3044.7,6026.7,7.5],"landmark":false,"img":{"s":[983,215],"p":[983,1279]}},{"id":"2:IV.12","label":"IV.12","course":"2","kind":"Satz","chapter":"IV","name":null,"page":71,"title":"Charakterisierungen von Untermannigfaltigkeiten","note":null,"deps":["2:IV.11","2:IV.10","2:IV.6"],"links":["2:IV.11","2:IV.10"],"implied":[{"id":"2:IV.6","via":"2:IV.10"}],"depth":31,"weight":17,"pos":[3089.4,6052.7,12.2],"landmark":false,"img":{"s":[983,2858]}},{"id":"2:III.20","label":"III.20","course":"2","kind":"Satz","chapter":"III","name":null,"page":39,"title":"Charakterisierungen der Konvexität","note":null,"deps":["2:III.19","2:III.14","2:III.17","1:VIII.22"],"links":["2:III.19","2:III.17","1:VIII.22"],"implied":[{"id":"2:III.14","via":"2:III.17"}],"depth":31,"weight":1,"pos":[4071,5597.5,7.5],"landmark":false,"img":{"s":[983,450],"p":[983,1709]}},{"id":"3:III.3","label":"III.3","course":"3","kind":"Lemma","chapter":"III","name":null,"page":36,"title":"Approximation durch dyadische Würfel","note":null,"deps":["3:III.2","1:IV.16"],"links":["3:III.2"],"implied":[{"id":"1:IV.16","via":"3:III.2"}],"depth":32,"weight":37,"pos":[2733.1,9139.8,15.1],"landmark":false,"img":{"s":[983,620],"p":[983,911]}},{"id":"3:V.3","label":"V.3","course":"3","kind":"Satz","chapter":"V","name":null,"page":60,"title":"Riemann-integrierbar ⇔ fast überall stetig","note":null,"deps":["3:V.2","3:IV.10","3:III.2","1:X.3","1:X.14"],"links":["3:V.2","3:III.2","1:X.14"],"implied":[{"id":"3:IV.10","via":"3:V.2"},{"id":"1:X.3","via":"1:X.14"}],"depth":32,"weight":0,"pos":[4599.3,8823.1,6],"landmark":false,"img":{"s":[983,140],"p":[983,992]}},{"id":"3:V.4","label":"V.4","course":"3","kind":"Satz","chapter":"V","name":null,"page":61,"title":"Stetigkeit parameterabhängiger Integrale","note":null,"deps":["3:V.2","2:I.19"],"links":["3:V.2","2:I.19"],"implied":[],"depth":32,"weight":7,"pos":[4746.4,8853.8,10],"landmark":false,"img":{"s":[983,335],"p":[983,338]}},{"id":"3:V.5","label":"V.5","course":"3","kind":"Satz","chapter":"V","name":null,"page":62,"title":"Differentiation parameterabhängiger Integrale","note":null,"deps":["3:V.2","1:VIII.13"],"links":["3:V.2","1:VIII.13"],"implied":[],"depth":32,"weight":5,"pos":[4803.5,8823.9,9.4],"landmark":false,"img":{"s":[983,410],"p":[983,272]}},{"id":"3:V.13","label":"V.13","course":"3","kind":"Lemma","chapter":"V","name":null,"page":66,"title":"Absolut konvergente Reihen in Lᵖ","note":null,"deps":["3:IV.10","3:V.12","3:IV.8","3:V.2"],"links":["3:V.12","3:V.2"],"implied":[{"id":"3:IV.10","via":"3:V.2"},{"id":"3:IV.8","via":"3:V.2"}],"depth":32,"weight":11,"pos":[4646.6,8810.6,11],"landmark":false,"img":{"s":[983,226],"p":[983,676]}},{"id":"3:V.20","label":"V.20","course":"3","kind":"Satz","chapter":"V","name":"Vitali","page":73,"title":"Satz von Vitali","note":null,"deps":["3:IV.7","3:I.21","3:V.2"],"links":["3:I.21","3:V.2"],"implied":[{"id":"3:IV.7","via":"3:V.2"}],"depth":32,"weight":0,"pos":[4695.6,8812.5,6],"landmark":false,"img":{"s":[983,343],"p":[983,2417]}},{"id":"3:VI.4","label":"VI.4","course":"3","kind":"Satz","chapter":"VI","name":"Cavalierische Prinzip","page":78,"title":"Prinzip von Cavalieri","note":null,"deps":["3:VI.3","3:II.8","3:V.2","3:IV.10"],"links":["3:VI.3","3:V.2"],"implied":[{"id":"3:II.8","via":"3:V.2"},{"id":"3:IV.10","via":"3:VI.3"}],"depth":32,"weight":16,"pos":[3379.4,8695,12],"landmark":false,"img":{"s":[983,245],"p":[983,3450]}},{"id":"2:V.36","label":"V.36","course":"2","kind":"Satz","chapter":"V","name":"Satz von Liouville","page":100,"title":"Satz von Liouville","note":null,"deps":["2:V.35"],"links":["2:V.35"],"implied":[],"depth":32,"weight":0,"pos":[5009.4,5967.3,6],"landmark":false,"img":{"s":[983,70],"p":[983,1022]}},{"id":"2:III.30","label":"III.30","course":"2","kind":"Satz","chapter":"III","name":null,"page":48,"title":"Taylorpolynom approximiert in Ordnung k","note":null,"deps":["2:III.29","2:III.24"],"links":["2:III.29","2:III.24"],"implied":[],"depth":32,"weight":0,"pos":[4201.7,5498.5,6],"landmark":false,"img":{"s":[983,175],"p":[983,2707]}},{"id":"3:X.10","label":"X.10","course":"3","kind":"Definition","chapter":"X","name":"Schwartz-Raum","page":126,"title":"Schwartz-Raum","note":null,"deps":["2:II.3","2:III.29"],"links":["2:III.29"],"implied":[{"id":"2:II.3","via":"2:III.29"}],"depth":32,"weight":1,"pos":[4006.5,8745.2,7.5],"landmark":false,"img":{"s":[983,398]}},{"id":"2:VI.23","label":"VI.23","course":"2","kind":"Satz","chapter":"VI","name":null,"page":124,"title":"exp(tA) löst Ẋ = AX","note":null,"deps":["2:VI.22","1:IX.7","2:VI.6"],"links":["2:VI.22","1:IX.7","2:VI.6"],"implied":[],"depth":32,"weight":4,"pos":[4447.4,6170.7,9],"landmark":true,"img":{"s":[983,70],"p":[983,352]}},{"id":"2:VI.11","label":"VI.11","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":112,"title":"Maximale Lösungen verlassen jedes Kompaktum","note":null,"deps":["2:VI.10","2:VI.6","2:I.15"],"links":["2:VI.10","2:VI.6"],"implied":[{"id":"2:I.15","via":"2:VI.10"}],"depth":32,"weight":11,"pos":[4379.8,6158.9,11],"landmark":false,"img":{"s":[983,320],"p":[983,1180]}},{"id":"2:VI.16","label":"VI.16","course":"2","kind":"Definition","chapter":"VI","name":null,"page":117,"title":"Stetige Abhängigkeit von den Daten","note":null,"deps":["2:VI.10"],"links":["2:VI.10"],"implied":[],"depth":32,"weight":3,"pos":[4496.9,6168.7,8.6],"landmark":false,"img":{"s":[983,478]}},{"id":"2:IV.14","label":"IV.14","course":"2","kind":"Satz","chapter":"IV","name":null,"page":73,"title":"Tangentialraum als Kern bzw. Bild","note":null,"deps":["2:IV.13","2:IV.12","L:9.21"],"links":["2:IV.13","2:IV.12"],"implied":[{"id":"L:9.21","via":"2:IV.12"}],"depth":32,"weight":1,"pos":[3049.6,6107.5,7.5],"landmark":false,"img":{"s":[983,274],"p":[983,1534]}},{"id":"3:VIII.5","label":"VIII.5","course":"3","kind":"Satz","chapter":"VIII","name":null,"page":100,"title":"Charakterisierungen von Untermannigfaltigkeiten","note":null,"deps":["3:VIII.4","2:IV.12"],"links":["3:VIII.4","2:IV.12"],"implied":[],"depth":32,"weight":13,"pos":[5015.6,8103.8,11.4],"landmark":false,"img":{"s":[983,347]}},{"id":"3:IX.1","label":"IX.1","course":"3","kind":"Satz","chapter":"IX","name":null,"page":106,"title":"Gebiete mit C¹-Rand","note":null,"deps":["3:VII.1","2:IV.10","2:IV.12"],"links":["3:VII.1","2:IV.12"],"implied":[{"id":"2:IV.10","via":"2:IV.12"}],"depth":32,"weight":6,"pos":[3749.3,8199.3,9.7],"landmark":false,"img":{"s":[983,582],"p":[983,42]}},{"id":"2:IV.9","label":"IV.9","course":"2","kind":"Satz","chapter":"IV","name":"Youngsche Ungleichung","page":67,"title":"Youngsche Ungleichung","note":null,"deps":["2:IV.8","2:IV.6","2:III.20","2:III.17"],"links":["2:IV.8","2:III.20"],"implied":[{"id":"2:IV.6","via":"2:IV.8"},{"id":"2:III.17","via":"2:III.20"}],"depth":32,"weight":0,"pos":[3134.2,6091.7,6],"landmark":false,"img":{"s":[983,234],"p":[983,2395]}},{"id":"3:III.4","label":"III.4","course":"3","kind":"Lemma","chapter":"III","name":null,"page":37,"title":"Borel-σ-Algebra und ihre Erzeuger","note":null,"deps":["3:III.3","3:II.24","3:I.3","1:IV.17"],"links":["3:III.3","3:II.24","1:IV.17"],"implied":[{"id":"3:I.3","via":"3:III.3"}],"depth":33,"weight":36,"pos":[2794.2,9151,15],"landmark":false,"img":{"s":[983,127],"p":[983,729]}},{"id":"3:V.6","label":"V.6","course":"3","kind":"Lemma","chapter":"V","name":null,"page":62,"title":"Differentiation unter dem Integral im ℝⁿ","note":null,"deps":["3:V.5","3:V.4","3:V.2","2:II.14"],"links":["3:V.5","3:V.4","2:II.14"],"implied":[{"id":"3:V.2","via":"3:V.5"}],"depth":33,"weight":4,"pos":[4781.4,8909.7,9],"landmark":false,"img":{"s":[983,530],"p":[983,2076]}},{"id":"3:V.14","label":"V.14","course":"3","kind":"Satz","chapter":"V","name":"Satz von Riesz-Fischer","page":67,"title":"Satz von Riesz-Fischer: Lᵖ ist vollständig","note":null,"deps":["3:V.13","2:IV.4"],"links":["3:V.13","2:IV.4"],"implied":[],"depth":33,"weight":10,"pos":[4729.7,8909.2,10.7],"landmark":true,"img":{"s":[983,67],"p":[983,1409]}},{"id":"3:VI.7","label":"VI.7","course":"3","kind":"Satz","chapter":"VI","name":"Fubini","page":83,"title":"Satz von Fubini","note":null,"deps":["3:VI.4","3:IV.9","3:IV.10","3:VI.6"],"links":["3:VI.4","3:VI.6"],"implied":[{"id":"3:IV.9","via":"3:VI.4"},{"id":"3:IV.10","via":"3:VI.4"}],"depth":33,"weight":14,"pos":[3380.8,8799.8,11.6],"landmark":true,"img":{"s":[983,611],"p":[983,4174]}},{"id":"2:VI.14","label":"VI.14","course":"2","kind":"Satz","chapter":"VI","name":"Langzeitexistenz bei linearem Wachstum","page":115,"title":"Langzeitexistenz bei linearem Wachstum","note":null,"deps":["2:VI.12","2:VI.11","2:VI.10"],"links":["2:VI.12","2:VI.11"],"implied":[{"id":"2:VI.10","via":"2:VI.11"}],"depth":33,"weight":6,"pos":[4506.6,6229.5,9.7],"landmark":false,"img":{"s":[983,301],"p":[983,1081]}},{"id":"2:VI.15","label":"VI.15","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":116,"title":"Langzeitexistenz bei ⟨x, f⟩ ≤ ω‖x‖²","note":null,"deps":["2:VI.11","2:VI.10","2:VI.12","1:VIII.14"],"links":["2:VI.11","2:VI.12"],"implied":[{"id":"2:VI.10","via":"2:VI.11"},{"id":"1:VIII.14","via":"2:VI.11"}],"depth":33,"weight":0,"pos":[4413.8,6231.6,6],"landmark":false,"img":{"s":[983,173],"p":[983,1203]}},{"id":"2:VI.17","label":"VI.17","course":"2","kind":"Satz","chapter":"VI","name":null,"page":117,"title":"Lösungen hängen stetig von (t₀, x₀, f) ab","note":null,"deps":["2:VI.16","2:VI.9","2:VI.12","2:VI.7","2:VI.11","2:III.8"],"links":["2:VI.16","2:VI.12","2:VI.11"],"implied":[{"id":"2:VI.9","via":"2:VI.16"},{"id":"2:VI.7","via":"2:VI.16"},{"id":"2:III.8","via":"2:VI.16"}],"depth":33,"weight":2,"pos":[4458.1,6218.6,8.1],"landmark":false,"img":{"s":[983,70],"p":[983,2171]}},{"id":"2:IV.15","label":"IV.15","course":"2","kind":"Satz","chapter":"IV","name":"Extrema mit Nebenbedingungen","page":75,"title":"Extrema unter Nebenbedingungen (Lagrange-Multiplikatoren)","note":null,"deps":["2:IV.14","2:IV.12","2:III.10"],"links":["2:IV.14","2:III.10"],"implied":[{"id":"2:IV.12","via":"2:IV.14"}],"depth":33,"weight":0,"pos":[3095.3,6160.9,6],"landmark":true,"img":{"s":[983,329],"p":[983,2448]}},{"id":"3:VIII.6","label":"VIII.6","course":"3","kind":"Satz","chapter":"VIII","name":null,"page":100,"title":"Untermannigfaltigkeiten sind σ-kompakt","note":null,"deps":["3:VIII.5","2:I.15","1:IV.20"],"links":["3:VIII.5","2:I.15"],"implied":[{"id":"1:IV.20","via":"3:VIII.5"}],"depth":33,"weight":9,"pos":[4985.2,8163.2,10.5],"landmark":false,"img":{"s":[983,130],"p":[983,878]}},{"id":"3:VIII.9","label":"VIII.9","course":"3","kind":"Satz","chapter":"VIII","name":null,"page":101,"title":"Parametrisierungen sind Homöomorphismen, Kartenwechsel","note":null,"deps":["3:VIII.5","3:VIII.7","2:IV.6"],"links":["3:VIII.5","3:VIII.7"],"implied":[{"id":"2:IV.6","via":"3:VIII.5"}],"depth":33,"weight":8,"pos":[5031.3,8188.7,10.2],"landmark":false,"img":{"s":[983,271],"p":[983,621]}},{"id":"3:IX.2","label":"IX.2","course":"3","kind":"Lemma","chapter":"IX","name":null,"page":107,"title":"Der Rand ist lokal ein Graph","note":null,"deps":["3:IX.1","3:VIII.5"],"links":["3:IX.1","3:VIII.5"],"implied":[],"depth":33,"weight":5,"pos":[3805.4,8243.6,9.4],"landmark":false,"img":{"s":[983,200],"p":[983,1050]}},{"id":"3:III.5","label":"III.5","course":"3","kind":"Satz","chapter":"III","name":null,"page":37,"title":"Grundeigenschaften des Lebesgue-Maßes","note":null,"deps":["3:II.31","3:III.4","3:III.2","1:IV.20"],"links":["3:III.4"],"implied":[{"id":"3:II.31","via":"3:III.4"},{"id":"3:III.2","via":"3:III.4"},{"id":"1:IV.20","via":"3:III.4"}],"depth":34,"weight":35,"pos":[2778.2,9224.5,14.9],"landmark":false,"img":{"s":[983,366],"p":[983,251]}},{"id":"3:V.15","label":"V.15","course":"3","kind":"Lemma","chapter":"V","name":null,"page":68,"title":"Lᵖ-Konvergenz ⇒ fast überall konvergente Teilfolge","note":null,"deps":["3:V.13","3:V.14"],"links":["3:V.14"],"implied":[{"id":"3:V.13","via":"3:V.14"}],"depth":34,"weight":2,"pos":[4794.5,8957,8.1],"landmark":false,"img":{"s":[983,478]}},{"id":"2:VI.20","label":"VI.20","course":"2","kind":"Definition","chapter":"VI","name":null,"page":120,"title":"Fundamentalsystem, Wronski-Determinante","note":null,"deps":["2:VI.2","2:VI.6","2:VI.14","L:9.23","L:12.17"],"links":["2:VI.2","2:VI.14","L:12.17"],"implied":[{"id":"2:VI.6","via":"2:VI.14"},{"id":"L:9.23","via":"L:12.17"}],"depth":34,"weight":5,"pos":[4487.2,6292,9.4],"landmark":false,"img":{"s":[983,621]}},{"id":"2:VI.18","label":"VI.18","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":119,"title":"Konvergenz der Lösungen bei konvergenten Daten","note":null,"deps":["2:VI.17"],"links":["2:VI.17"],"implied":[],"depth":34,"weight":1,"pos":[4439,6300,7.5],"landmark":false,"img":{"s":[983,550]}},{"id":"3:VIII.8","label":"VIII.8","course":"3","kind":"Lemma","chapter":"VIII","name":null,"page":101,"title":"Überdeckung durch abzählbar viele Parametrisierungen","note":null,"deps":["3:VIII.6","3:VIII.7"],"links":["3:VIII.6","3:VIII.7"],"implied":[],"depth":34,"weight":8,"pos":[5005.8,8246.1,10.2],"landmark":false,"img":{"s":[983,69],"p":[983,155]}},{"id":"3:IX.3","label":"IX.3","course":"3","kind":"Lemma","chapter":"IX","name":null,"page":108,"title":"Äußere Einheitsnormale","note":null,"deps":["3:IX.1","3:IX.2","2:IV.13"],"links":["3:IX.2","2:IV.13"],"implied":[{"id":"3:IX.1","via":"3:IX.2"}],"depth":34,"weight":4,"pos":[3756.7,8316.1,9],"landmark":false,"img":{"s":[983,197],"p":[983,1031]}},{"id":"3:III.6","label":"III.6","course":"3","kind":"Lemma","chapter":"III","name":null,"page":38,"title":"Regularität des Lebesgue-Maßes","note":null,"deps":["3:I.7","3:III.5","1:IV.20"],"links":["3:III.5"],"implied":[{"id":"3:I.7","via":"3:III.5"},{"id":"1:IV.20","via":"3:III.5"}],"depth":35,"weight":31,"pos":[2811,9281.3,14.4],"landmark":false,"img":{"s":[983,186],"p":[983,1360]}},{"id":"3:III.9","label":"III.9","course":"3","kind":"Definition","chapter":"III","name":null,"page":41,"title":"Borel-Maß","note":null,"deps":["3:III.5","3:II.1"],"links":["3:III.5"],"implied":[{"id":"3:II.1","via":"3:III.5"}],"depth":35,"weight":21,"pos":[2751.9,9278.1,12.9],"landmark":false,"img":{"s":[983,310]}},{"id":"2:VI.21","label":"VI.21","course":"2","kind":"Satz","chapter":"VI","name":null,"page":121,"title":"Formel von Liouville für die Wronski-Determinante","note":null,"deps":["2:VI.20","2:II.11","1:VIII.15","L:12.10","L:12.16"],"links":["2:VI.20","1:VIII.15"],"implied":[{"id":"2:II.11","via":"2:VI.20"},{"id":"L:12.10","via":"2:VI.20"},{"id":"L:12.16","via":"2:VI.20"}],"depth":35,"weight":4,"pos":[4393.7,6339.2,9],"landmark":false,"img":{"s":[983,251],"p":[983,4176]}},{"id":"2:VI.19","label":"VI.19","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":119,"title":"Vergleichssatz (nicht strikt)","note":null,"deps":["2:VI.13","2:VI.17","2:VI.18"],"links":["2:VI.13","2:VI.18"],"implied":[{"id":"2:VI.17","via":"2:VI.18"}],"depth":35,"weight":0,"pos":[4471.3,6352.3,6],"landmark":false,"img":{"s":[983,393],"p":[983,1076]}},{"id":"3:III.7","label":"III.7","course":"3","kind":"Satz","chapter":"III","name":null,"page":39,"title":"Lebesgue-messbar ⇔ Borel bis auf Nullmenge","note":null,"deps":["3:II.18","3:III.6"],"links":["3:III.6"],"implied":[{"id":"3:II.18","via":"3:III.6"}],"depth":36,"weight":25,"pos":[2834.6,9356.8,13.5],"landmark":false,"img":{"s":[983,219],"p":[983,868]}},{"id":"3:III.8","label":"III.8","course":"3","kind":"Satz","chapter":"III","name":"Satz von Lusin","page":40,"title":"Satz von Lusin","note":null,"deps":["3:III.6","3:I.7","3:I.21","1:VI.1"],"links":["3:III.6","3:I.21","1:VI.1"],"implied":[{"id":"3:I.7","via":"3:III.6"}],"depth":36,"weight":0,"pos":[2772.2,9324.8,6],"landmark":false,"img":{"s":[983,154],"p":[983,1291]}},{"id":"3:III.12","label":"III.12","course":"3","kind":"Lemma","chapter":"III","name":null,"page":42,"title":"Lipschitz-Abbildungen und Lebesgue-Maß","note":null,"deps":["3:III.6","3:III.3","2:I.18"],"links":["3:III.6","2:I.18"],"implied":[{"id":"3:III.3","via":"3:III.6"}],"depth":36,"weight":20,"pos":[2687.7,9381.7,12.7],"landmark":false,"img":{"s":[983,122],"p":[983,802]}},{"id":"3:V.17","label":"V.17","course":"3","kind":"Satz","chapter":"V","name":null,"page":69,"title":"C_c⁰(Ω) ist dicht in Lᵖ(Ω)","note":null,"deps":["3:V.16","3:III.6","3:IV.9","3:V.2","3:IV.7","3:V.14"],"links":["3:V.16","3:III.6","3:V.14"],"implied":[{"id":"3:IV.9","via":"3:V.2"},{"id":"3:V.2","via":"3:V.14"},{"id":"3:IV.7","via":"3:V.2"}],"depth":36,"weight":8,"pos":[4639,9049.9,10.2],"landmark":false,"img":{"s":[983,159],"p":[983,2553]}},{"id":"3:III.10","label":"III.10","course":"3","kind":"Lemma","chapter":"III","name":null,"page":41,"title":"Koordinatenhyperebenen sind Nullmengen","note":null,"deps":["3:III.9","3:I.7"],"links":["3:III.9"],"implied":[{"id":"3:I.7","via":"3:III.9"}],"depth":36,"weight":20,"pos":[2722.9,9336.3,12.7],"landmark":false,"img":{"s":[983,135],"p":[983,373]}},{"id":"2:VI.24","label":"VI.24","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":124,"title":"Rechenregeln der Matrix-Exponentialfunktion","note":null,"deps":["2:VI.23","2:VI.21","2:VI.6"],"links":["2:VI.23","2:VI.21"],"implied":[{"id":"2:VI.6","via":"2:VI.23"}],"depth":36,"weight":3,"pos":[4458.9,6412,8.6],"landmark":false,"img":{"s":[983,417],"p":[983,739]}},{"id":"3:VI.5","label":"VI.5","course":"3","kind":"Lemma","chapter":"VI","name":null,"page":80,"title":"λⁿ = λᵏ × λᵐ","note":null,"deps":["3:VI.4","3:III.7","3:III.2","3:II.15"],"links":["3:VI.4","3:III.7"],"implied":[{"id":"3:III.2","via":"3:III.7"},{"id":"3:II.15","via":"3:III.7"}],"depth":37,"weight":12,"pos":[3360.2,8993,11.2],"landmark":false,"img":{"s":[983,42],"p":[983,2831]}},{"id":"3:III.13","label":"III.13","course":"3","kind":"Satz","chapter":"III","name":null,"page":43,"title":"C¹-Abbildungen erhalten Nullmengen und Messbarkeit","note":null,"deps":["3:III.3","3:III.12","3:III.7","2:III.8"],"links":["3:III.12","3:III.7","2:III.8"],"implied":[{"id":"3:III.3","via":"3:III.12"}],"depth":37,"weight":19,"pos":[2746.4,9437,12.5],"landmark":false,"img":{"s":[983,127],"p":[983,372]}},{"id":"3:V.18","label":"V.18","course":"3","kind":"Satz","chapter":"V","name":null,"page":71,"title":"Fourierreihen konvergieren in L²","note":null,"deps":["3:V.17","3:V.15","3:V.9","1:V.18"],"links":["3:V.17","3:V.15","3:V.9","1:V.18"],"implied":[],"depth":37,"weight":1,"pos":[4775.8,9108.6,7.5],"landmark":false,"img":{"s":[983,42],"p":[983,1441]}},{"id":"3:III.11","label":"III.11","course":"3","kind":"Satz","chapter":"III","name":null,"page":42,"title":"Translationsinvariante Borel-Maße sind Vielfache von λⁿ","note":null,"deps":["3:III.10","3:III.3","3:II.17"],"links":["3:III.10"],"implied":[{"id":"3:III.3","via":"3:III.10"},{"id":"3:II.17","via":"3:III.10"}],"depth":37,"weight":19,"pos":[2797.2,9411.1,12.5],"landmark":false,"img":{"s":[983,137],"p":[983,561]}},{"id":"2:VI.25","label":"VI.25","course":"2","kind":"Lemma","chapter":"VI","name":null,"page":125,"title":"Fundamentalsystem bei diagonalisierbarem A","note":null,"deps":["2:VI.23","2:VI.24","L:14.3"],"links":["2:VI.24","L:14.3"],"implied":[{"id":"2:VI.23","via":"2:VI.24"}],"depth":37,"weight":0,"pos":[4436.8,6474.8,6],"landmark":false,"img":{"s":[983,171],"p":[983,1937]}},{"id":"2:VI.26","label":"VI.26","course":"2","kind":"Satz","chapter":"VI","name":null,"page":127,"title":"Fundamentalsystem im allgemeinen Fall (Jordan)","note":null,"deps":["2:VI.23","2:VI.24","L:17.13"],"links":["2:VI.24","L:17.13"],"implied":[{"id":"2:VI.23","via":"2:VI.24"}],"depth":37,"weight":1,"pos":[4482.3,6474.5,7.5],"landmark":false,"img":{"s":[983,7254]}},{"id":"3:VI.8","label":"VI.8","course":"3","kind":"Satz","chapter":"VI","name":null,"page":86,"title":"Partielle Integration im ℝⁿ","note":null,"deps":["3:VI.5","3:VI.7","3:V.16","1:XI.5"],"links":["3:VI.5","3:VI.7","3:V.16","1:XI.5"],"implied":[],"depth":38,"weight":4,"pos":[3392.5,9065.9,9],"landmark":false,"img":{"s":[983,129],"p":[983,1793]}},{"id":"3:X.1","label":"X.1","course":"3","kind":"Satz","chapter":"X","name":null,"page":119,"title":"Faltung und Youngsche Faltungsungleichung","note":null,"deps":["3:VI.7","3:VI.5","3:V.11","3:V.12"],"links":["3:VI.7","3:VI.5","3:V.12"],"implied":[{"id":"3:V.11","via":"3:V.12"}],"depth":38,"weight":7,"pos":[4009.1,9747.5,10],"landmark":true,"img":{"s":[983,205],"p":[983,1057]}},{"id":"3:V.19","label":"V.19","course":"3","kind":"Lemma","chapter":"V","name":null,"page":72,"title":"Fourierkoeffizienten: Isometrie L² → ℓ²","note":null,"deps":["3:V.18"],"links":["3:V.18"],"implied":[],"depth":38,"weight":0,"pos":[4777.2,9177.8,6],"landmark":false,"img":{"s":[983,135],"p":[983,910]}},{"id":"3:III.14","label":"III.14","course":"3","kind":"Satz","chapter":"III","name":null,"page":43,"title":"Invarianz unter Bewegungen","note":null,"deps":["3:III.5","3:III.13","3:III.11","3:III.6","L:18.54","L:12.16"],"links":["3:III.13","3:III.11","L:18.54","L:12.16"],"implied":[{"id":"3:III.5","via":"3:III.13"},{"id":"3:III.6","via":"3:III.13"}],"depth":38,"weight":18,"pos":[2733.6,9499.2,12.4],"landmark":false,"img":{"s":[983,93],"p":[983,1229]}},{"id":"2:VI.27","label":"VI.27","course":"2","kind":"Satz","chapter":"VI","name":null,"page":131,"title":"Lineare Gleichungen mit konstanten Koeffizienten","note":null,"deps":["2:VI.26","2:VI.20","1:IV.29"],"links":["2:VI.26","1:IV.29"],"implied":[{"id":"2:VI.20","via":"2:VI.26"}],"depth":38,"weight":0,"pos":[4459.5,6536.7,6],"landmark":false,"img":{"s":[983,225],"p":[983,2904]}},{"id":"3:X.4","label":"X.4","course":"3","kind":"Satz","chapter":"X","name":null,"page":121,"title":"Glattheit von Faltungen","note":null,"deps":["3:V.4","3:V.6","3:X.1"],"links":["3:V.6","3:X.1"],"implied":[{"id":"3:V.4","via":"3:V.6"}],"depth":39,"weight":3,"pos":[4016.5,9819.7,8.6],"landmark":false,"img":{"s":[983,199],"p":[983,966]}},{"id":"3:X.7","label":"X.7","course":"3","kind":"Satz","chapter":"X","name":null,"page":123,"title":"Grundeigenschaften der Fourier-Transformation","note":null,"deps":["3:X.6","3:V.4","3:VI.7","3:X.1"],"links":["3:X.6","3:V.4","3:X.1"],"implied":[{"id":"3:VI.7","via":"3:X.1"}],"depth":39,"weight":3,"pos":[4059.1,9844.5,8.6],"landmark":false,"img":{"s":[983,176],"p":[983,2526]}},{"id":"3:III.16","label":"III.16","course":"3","kind":"Satz","chapter":"III","name":"Lineare Transformationsformel","page":45,"title":"Lineare Transformationsformel","note":null,"deps":["3:III.10","3:III.15","3:III.14"],"links":["3:III.15","3:III.14"],"implied":[{"id":"3:III.10","via":"3:III.14"}],"depth":39,"weight":11,"pos":[2786.7,9546,11],"landmark":true,"img":{"s":[983,98],"p":[983,2387]}},{"id":"3:X.2","label":"X.2","course":"3","kind":"Lemma","chapter":"X","name":null,"page":120,"title":"Stetigkeit der Translation in Lᵖ","note":null,"deps":["3:V.17","3:III.14"],"links":["3:V.17","3:III.14"],"implied":[],"depth":39,"weight":5,"pos":[3970.7,9839.6,9.4],"landmark":false,"img":{"s":[983,216],"p":[983,79]}},{"id":"3:VII.2","label":"VII.2","course":"3","kind":"Lemma","chapter":"VII","name":null,"page":88,"title":"Volumenverzerrung kleiner Würfel","note":null,"deps":["3:III.16","2:II.7","2:III.7"],"links":["3:III.16"],"implied":[{"id":"2:II.7","via":"3:III.16"},{"id":"2:III.7","via":"3:III.16"}],"depth":40,"weight":10,"pos":[4115.1,9266.5,10.7],"landmark":false,"img":{"s":[983,178],"p":[983,1257]}},{"id":"3:X.3","label":"X.3","course":"3","kind":"Satz","chapter":"X","name":null,"page":120,"title":"Approximation durch Glättung (Dirac-Folgen)","note":null,"deps":["3:X.1","3:X.2","3:V.2","3:VI.7"],"links":["3:X.1","3:X.2"],"implied":[{"id":"3:V.2","via":"3:X.1"},{"id":"3:VI.7","via":"3:X.1"}],"depth":40,"weight":4,"pos":[4010.9,9886,9],"landmark":false,"img":{"s":[983,140],"p":[983,1324]}},{"id":"3:VII.3","label":"VII.3","course":"3","kind":"Satz","chapter":"VII","name":"Transformationsformel","page":89,"title":"Transformationsformel","note":null,"deps":["3:VII.1","3:VII.2","3:III.13","3:III.7","3:III.3","3:III.16","3:IV.9","3:IV.10","3:I.7","2:IV.6"],"links":["3:VII.1","3:VII.2","3:IV.10","2:IV.6"],"implied":[{"id":"3:III.13","via":"3:VII.2"},{"id":"3:III.7","via":"3:VII.2"},{"id":"3:III.3","via":"3:VII.2"},{"id":"3:III.16","via":"3:VII.2"},{"id":"3:IV.9","via":"3:IV.10"},{"id":"3:I.7","via":"3:VII.2"}],"depth":41,"weight":9,"pos":[4017.4,9270.1,10.5],"landmark":true,"img":{"s":[983,436],"p":[983,7135]}},{"id":"3:X.5","label":"X.5","course":"3","kind":"Satz","chapter":"X","name":null,"page":122,"title":"C_c^∞(Ω) ist dicht in Lᵖ(Ω)","note":null,"deps":["3:V.17","3:X.4","3:X.3"],"links":["3:X.4","3:X.3"],"implied":[{"id":"3:V.17","via":"3:X.3"}],"depth":41,"weight":2,"pos":[3984.6,9974.8,8.1],"landmark":false,"img":{"s":[983,71],"p":[983,412]}},{"id":"3:X.8","label":"X.8","course":"3","kind":"Satz","chapter":"X","name":"Plancherel","page":125,"title":"Satz von Plancherel","note":null,"deps":["3:X.3","3:X.7","3:VI.7"],"links":["3:X.3","3:X.7"],"implied":[{"id":"3:VI.7","via":"3:X.3"}],"depth":41,"weight":2,"pos":[4025.7,9949.6,8.1],"landmark":true,"img":{"s":[983,48],"p":[983,1067]}},{"id":"3:VIII.3","label":"VIII.3","course":"3","kind":"Satz","chapter":"VIII","name":null,"page":99,"title":"Invarianz unter Umparametrisierung","note":null,"deps":["3:VIII.2","3:VII.3","2:II.11"],"links":["3:VIII.2","3:VII.3"],"implied":[{"id":"2:II.11","via":"3:VII.3"}],"depth":42,"weight":8,"pos":[4960.6,9341.3,10.2],"landmark":false,"img":{"s":[983,126],"p":[983,378]}},{"id":"3:X.9","label":"X.9","course":"3","kind":"Satz","chapter":"X","name":null,"page":125,"title":"Fourier-Transformation auf L²","note":null,"deps":["3:X.7","3:X.8","3:V.14","3:X.5"],"links":["3:X.8","3:X.5"],"implied":[{"id":"3:X.7","via":"3:X.8"},{"id":"3:V.14","via":"3:X.8"}],"depth":42,"weight":1,"pos":[4035.9,10027.1,7.5],"landmark":false,"img":{"s":[983,440],"p":[983,708]}},{"id":"3:VIII.10","label":"VIII.10","course":"3","kind":"Satz","chapter":"VIII","name":"Flächenmaß","page":102,"title":"Flächenmaß auf Untermannigfaltigkeiten","note":null,"deps":["3:VIII.8","3:VIII.9","3:VIII.3","3:II.7"],"links":["3:VIII.8","3:VIII.9","3:VIII.3"],"implied":[{"id":"3:II.7","via":"3:VIII.3"}],"depth":43,"weight":7,"pos":[4998.6,9377.1,10],"landmark":true,"img":{"s":[983,243],"p":[983,1332]}},{"id":"3:X.11","label":"X.11","course":"3","kind":"Satz","chapter":"X","name":null,"page":127,"title":"Fourier-Transformation auf dem Schwartz-Raum, Umkehrformel","note":null,"deps":["3:X.7","3:X.9","3:X.10","3:V.6","3:VI.8"],"links":["3:X.9","3:X.10","3:VI.8"],"implied":[{"id":"3:X.7","via":"3:X.9"},{"id":"3:V.6","via":"3:X.9"}],"depth":43,"weight":0,"pos":[4008.1,10069.4,6],"landmark":false,"img":{"s":[983,137],"p":[983,2586]}},{"id":"3:VIII.11","label":"VIII.11","course":"3","kind":"Satz","chapter":"VIII","name":"Oberflächenintegral","page":103,"title":"Oberflächenintegral","note":null,"deps":["3:VIII.10","3:IV.3"],"links":["3:VIII.10"],"implied":[{"id":"3:IV.3","via":"3:VIII.10"}],"depth":44,"weight":6,"pos":[4873.6,9459.5,9.7],"landmark":false,"img":{"s":[983,245],"p":[983,225]}},{"id":"3:VIII.12","label":"VIII.12","course":"3","kind":"Lemma","chapter":"VIII","name":null,"page":103,"title":"Flächenmaß unter Ähnlichkeitsabbildungen","note":null,"deps":["3:VIII.10","3:VIII.11"],"links":["3:VIII.11"],"implied":[{"id":"3:VIII.10","via":"3:VIII.11"}],"depth":45,"weight":0,"pos":[5008,9534,6],"landmark":false,"img":{"s":[983,552],"p":[983,721]}},{"id":"3:VIII.13","label":"VIII.13","course":"3","kind":"Satz","chapter":"VIII","name":"Zwiebelformel","page":104,"title":"Zwiebelformel","note":null,"deps":["3:VIII.11","3:VII.3","3:VI.7"],"links":["3:VIII.11","3:VI.7"],"implied":[{"id":"3:VII.3","via":"3:VIII.11"}],"depth":45,"weight":1,"pos":[4899.9,9522.2,7.5],"landmark":false,"img":{"s":[983,259],"p":[983,1708]}},{"id":"3:IX.5","label":"IX.5","course":"3","kind":"Lemma","chapter":"IX","name":null,"page":109,"title":"Gaußscher Satz für Gebiete unter einem Graphen","note":null,"deps":["3:VI.7","3:VIII.11","3:IX.3","3:IX.4","2:II.11","1:XI.5"],"links":["3:VI.7","3:VIII.11","3:IX.3","3:IX.4"],"implied":[{"id":"2:II.11","via":"3:VIII.11"},{"id":"1:XI.5","via":"3:VIII.11"}],"depth":45,"weight":3,"pos":[3774.9,9564.1,8.6],"landmark":false,"img":{"s":[983,160],"p":[983,1533]}},{"id":"3:IX.7","label":"IX.7","course":"3","kind":"Satz","chapter":"IX","name":"Integralsatz von Gauß","page":111,"title":"Integralsatz von Gauß","note":null,"deps":["3:IX.1","3:IX.6","3:IX.5","3:VI.8","3:VIII.11"],"links":["3:IX.6","3:IX.5","3:VI.8"],"implied":[{"id":"3:IX.1","via":"3:IX.5"},{"id":"3:VIII.11","via":"3:IX.5"}],"depth":46,"weight":2,"pos":[3770.6,9627.9,8.1],"landmark":true,"img":{"s":[983,276],"p":[983,1004]}},{"id":"3:IX.8","label":"IX.8","course":"3","kind":"Lemma","chapter":"IX","name":"Greensche Formeln","page":112,"title":"Greensche Formeln","note":null,"deps":["3:IX.7","3:VIII.13"],"links":["3:IX.7","3:VIII.13"],"implied":[],"depth":47,"weight":0,"pos":[3766.3,9719.2,6],"landmark":false,"img":{"s":[983,318],"p":[983,2775]}},{"id":"3:IX.9","label":"IX.9","course":"3","kind":"Satz","chapter":"IX","name":"Satz von Stokes, klassische Version","page":114,"title":"Satz von Stokes (klassisch)","note":null,"deps":["3:IX.10","3:IX.7","3:VIII.11","2:V.8"],"links":["3:IX.10","3:IX.7","2:V.8"],"implied":[{"id":"3:VIII.11","via":"3:IX.7"}],"depth":47,"weight":0,"pos":[3805.2,9698.6,6],"landmark":true,"img":{"s":[983,738]}}],"size":[7515.2,10335.4],"territories":{"1:0":{"path":"M1999.7,472L2008,469.4L2024,462.6L2036,456L2040,453.7L2056,442.7L2059.3,440L2072,428.7L2076.7,424L2088,410.9L2090.3,408L2101.1,392L2104,386.7L2109.7,376L2116.3,360L2120,348L2121.2,344L2124.7,328L2126.7,312L2127.2,296L2126.3,280L2124,264L2120.1,248L2120,247.7L2114.8,232L2107.7,216L2104,209.3L2098.6,200L2088,185.1L2087.2,184L2072.8,168L2072,167.2L2056,153.3L2054.2,152L2040,142.2L2028.7,136L2024,133.5L2008,126.6L1992,121.5L1985,120L1976,117.9L1960,115.8L1944,115.1L1928,115.9L1912,118.1L1903.6,120L1896,121.7L1880,126.8L1864,133.8L1859.9,136L1848,142.6L1834.5,152L1832,153.8L1816,167.9L1815.9,168L1801.5,184L1800,185.9L1790,200L1784,210.5L1780.9,216L1773.8,232L1768.5,248L1768,250.2L1764.7,264L1762.3,280L1761.4,296L1762,312L1763.9,328L1767.4,344L1768,345.8L1772.3,360L1779,376L1784,385.5L1787.6,392L1798.4,408L1800,410.1L1811.9,424L1816,428.1L1829.3,440L1832,442.2L1848,453.3L1852.6,456L1864,462.2L1880,469.1L1888.9,472L1896,474.3L1912,478L1928,480.2L1944,480.9L1960,480.2L1976,478.1L1992,474.5L1999.7,472Z","label":[1936.3,290]},"1:I":{"path":"M1530,1368L1544,1364.9L1560,1360.5L1576,1354.7L1582.5,1352L1592,1347.7L1608,1339.1L1613,1336L1624,1330.2L1640,1320L1640,1320L1656,1308.1L1660.9,1304L1672,1294.4L1678.7,1288L1688,1279.2L1695.1,1272L1704,1262.1L1709.2,1256L1720,1242.3L1721.8,1240L1733.8,1224L1736,1220.5L1744.3,1208L1752,1194.7L1753.5,1192L1761.5,1176L1768,1160.1L1768,1160L1776,1144L1782.5,1128L1784,1123.7L1788.7,1112L1794.2,1096L1799.2,1080L1800,1076.9L1803.8,1064L1807.8,1048L1811.9,1032L1814.9,1016L1816,1009.5L1817.8,1000L1820.4,984L1822.8,968L1825.2,952L1827.4,936L1829.7,920L1831.9,904L1832,903.4L1835,888L1837.9,872L1840.9,856L1843.7,840L1846.4,824L1848,814.6L1849.1,808L1851.7,792L1854.2,776L1856.5,760L1858.5,744L1860.1,728L1861.4,712L1862.2,696L1862.6,680L1862.4,664L1861.8,648L1860.5,632L1858.6,616L1855.9,600L1852.4,584L1848,568.2L1847.9,568L1842.6,552L1835.9,536L1832,528.2L1828.1,520L1819.2,504L1816,499L1809.3,488L1800,475.2L1797.9,472L1786.1,456L1784,453.5L1773.4,440L1768,433.9L1757.7,424L1752,418.6L1740,408L1736,404.6L1720,392.2L1719.7,392L1704,380.2L1698,376L1688,368.9L1672.8,360L1672,359.5L1656,350.6L1641.9,344L1640,343L1624,334.9L1608,328.2L1607.5,328L1592,321.3L1576,315.5L1564.9,312L1560,310.3L1544,305.4L1528,301.3L1512,297.9L1501.4,296L1496,294.9L1480,292.1L1464,289.9L1448,288.3L1432,287.2L1416,286.7L1400,286.7L1384,287.3L1368,288.4L1352,290.3L1336,292.8L1320.7,296L1320,296.1L1304,299.4L1288,303.5L1272,308.6L1263,312L1256,314.4L1240,320.9L1225.6,328L1224,328.7L1208,336.9L1196,344L1192,346.1L1176,355.6L1169.5,360L1160,366.2L1146.8,376L1144,378.1L1128,392L1128,392L1112,406.4L1110.4,408L1096,422.8L1094.9,424L1080.9,440L1080,441.1L1068.4,456L1064,462.4L1057.5,472L1048.2,488L1048,488.4L1038.6,504L1032,517.2L1030.5,520L1022.7,536L1016.6,552L1016,553.7L1010.7,568L1006,584L1002.3,600L1000,612.5L999.3,616L996.9,632L995.2,648L994.1,664L993.6,680L993.6,696L994.1,712L995,728L996.4,744L998.2,760L1000,772.8L1000.4,776L1002.5,792L1004.8,808L1007.3,824L1010,840L1012.7,856L1015.6,872L1016,874.1L1018.1,888L1020.5,904L1022.9,920L1025.5,936L1028.1,952L1031,968L1032,973.4L1033.7,984L1036.9,1000L1040.4,1016L1044.5,1032L1048,1042.1L1049.6,1048L1054,1064L1059.4,1080L1064,1092.1L1065.3,1096L1071.3,1112L1078.5,1128L1080,1131.1L1086.3,1144L1095.6,1160L1096,1160.6L1105.4,1176L1112,1185.7L1116.1,1192L1128,1207.9L1128.1,1208L1139.8,1224L1144,1229.2L1152.9,1240L1160,1247.5L1168.6,1256L1176,1263.5L1184.7,1272L1192,1278.8L1202.8,1288L1208,1292.5L1222.8,1304L1224,1304.9L1240,1316.6L1245.3,1320L1256,1326.4L1272,1334.6L1274.9,1336L1288,1343.4L1304,1350.8L1306.9,1352L1320,1356.5L1336,1361.1L1352,1364.9L1368,1368L1368.1,1368L1384,1372.1L1400,1375.1L1416,1377.2L1432,1378.5L1448,1378.9L1464,1378.6L1480,1377.5L1496,1375.5L1512,1372.6L1528,1368.6L1530,1368Z","label":[1416.6,819.6]},"1:II":{"path":"M2541.3,1304L2552,1303L2568,1300.7L2584,1297.5L2600,1293.1L2614.5,1288L2616,1287.5L2632,1280.7L2648,1272L2648.1,1272L2664,1263.8L2676.3,1256L2680,1253.4L2696,1240.4L2696.4,1240L2712,1229.4L2719,1224L2728,1215.2L2734.9,1208L2744,1197.8L2749,1192L2760,1181.6L2765.7,1176L2776,1163.1L2778.5,1160L2790.7,1144L2792,1142.3L2803,1128L2808,1121L2814.6,1112L2824,1099.3L2826.5,1096L2837.6,1080L2840,1076.5L2847.7,1064L2856,1050.2L2857.6,1048L2868.2,1032L2872,1025.7L2878.1,1016L2886.7,1000L2888,997.4L2895,984L2901.9,968L2904,962.5L2908.8,952L2915.1,936L2920,921L2920.4,920L2925.7,904L2930.1,888L2933.8,872L2936,860.6L2937.1,856L2940.2,840L2942.6,824L2944.4,808L2945.7,792L2946.4,776L2946.5,760L2946.1,744L2945.2,728L2943.7,712L2941.5,696L2938.5,680L2936,669.2L2935,664L2931.2,648L2926.4,632L2920.5,616L2920,614.7L2915,600L2908.3,584L2904,575.2L2900.6,568L2891.3,552L2888,546.8L2881.6,536L2872,522.3L2870.4,520L2857.9,504L2856,501.8L2843.8,488L2840,484L2827.7,472L2824,468.6L2808.7,456L2808,455.5L2792,443.3L2787,440L2776,432.7L2760.4,424L2760,423.8L2744,415.4L2728,408.8L2725.7,408L2712,402.8L2696,398L2680,394.3L2665.9,392L2664,391.7L2648,389.8L2632,388.6L2616,388.3L2600,388.6L2584,389.8L2568,391.8L2566.7,392L2552,394.4L2536,397.8L2520,402.3L2504,407.9L2503.8,408L2488,414.3L2472,422.3L2469,424L2456,431L2442.4,440L2440,441.5L2424,453.1L2420.4,456L2408,465.6L2400.6,472L2392,480.1L2384.2,488L2376,496.9L2369.8,504L2360,516.2L2357.1,520L2345.4,536L2344,538.1L2334.7,552L2328,563.2L2325.1,568L2316.4,584L2312,593.4L2308.7,600L2301.5,616L2296,630.9L2295.6,632L2289.9,648L2285.2,664L2281.2,680L2280,685.6L2277.2,696L2273.6,712L2270.3,728L2267.9,744L2265.8,760L2264.2,776L2264,778.6L2262.6,792L2261.3,808L2260.3,824L2259.8,840L2259.5,856L2259.6,872L2259.8,888L2260.4,904L2261.1,920L2261.9,936L2263,952L2264,966.6L2264.1,968L2265.1,984L2266.1,1000L2267.3,1016L2268.8,1032L2270.4,1048L2272.3,1064L2274.8,1080L2277.6,1096L2280,1106.5L2281.1,1112L2284.9,1128L2290,1144L2296,1159.6L2296.1,1160L2302.9,1176L2311.8,1192L2312,1192.3L2321.6,1208L2328,1216.7L2333.6,1224L2344,1235.2L2348.9,1240L2360,1250.5L2366.6,1256L2376,1263L2390.5,1272L2392,1273L2408,1282L2421.4,1288L2424,1289.1L2440,1294.7L2456,1298.9L2472,1301.9L2488,1303.8L2490.6,1304L2504,1305.1L2520,1305.4L2536,1304.6L2541.3,1304Z","label":[2586.6,821.6]},"1:IV":{"path":"M786.4,3064L792,3063.4L808,3060.6L824,3056.8L840,3051.9L850.3,3048L856,3045.8L872,3038.4L883.6,3032L888,3029.9L904,3021.5L913.2,3016L920,3011.9L936,3001.1L937.5,3000L952,2991.8L964.3,2984L968,2981.7L984,2970.8L988,2968L1000,2958.9L1008.6,2952L1016,2946.1L1027.9,2936L1032,2932.5L1045.8,2920L1048,2918L1062.4,2904L1064,2902.5L1076.6,2888L1080,2883.6L1089.3,2872L1096,2862.7L1099.2,2856L1106.2,2840L1112,2824.9L1112.3,2824L1118.7,2808L1125.6,2792L1128,2786.1L1132.6,2776L1140,2760L1144,2751.5L1147.8,2744L1156.1,2728L1160,2720.3L1164.9,2712L1173.6,2696L1176,2688.8L1180.4,2680L1183.5,2664L1186.1,2648L1188.3,2632L1190.2,2616L1191.7,2600L1192,2596.5L1193.2,2584L1194.5,2568L1195.6,2552L1196.4,2536L1196.9,2520L1197.2,2504L1197.3,2488L1197.1,2472L1196.5,2456L1195.6,2440L1194.2,2424L1192.3,2408L1192,2406.1L1190.3,2392L1187.8,2376L1184.7,2360L1180.9,2344L1176.2,2328L1176,2327.4L1171.4,2312L1165.5,2296L1160,2283.5L1158.5,2280L1150.7,2264L1144,2252.7L1141.7,2248L1132.9,2232L1128,2224.1L1122.7,2216L1112,2201.8L1110.7,2200L1097.2,2184L1096,2182.6L1084.2,2168L1080,2163.1L1070.8,2152L1064,2143.1L1058.2,2136L1048,2122.4L1046.2,2120L1036.3,2104L1032,2093.4L1030.1,2088L1026.3,2072L1025.8,2056L1027.5,2040L1030.4,2024L1032,2016.9L1034.2,2008L1037,1992L1041.3,1976L1044.9,1960L1047.7,1944L1048,1941.6L1050.3,1928L1051.9,1912L1053.4,1896L1054.1,1880L1054.3,1864L1053.9,1848L1053,1832L1051.7,1816L1049.8,1800L1048,1787.8L1047.5,1784L1045.2,1768L1042.3,1752L1038.7,1736L1034.4,1720L1032,1712.3L1029.7,1704L1024.3,1688L1017.6,1672L1016,1668.6L1010.4,1656L1001.6,1640L1000,1637.4L991.7,1624L984,1613.5L979.8,1608L968,1594.4L965.7,1592L952,1578.8L948.7,1576L936,1566.3L926.1,1560L920,1555.9L904,1547.1L896.9,1544L888,1539.9L872,1534.3L856,1530.4L841,1528L840,1527.8L824,1526.4L808,1526.3L792,1527.6L789.4,1528L776,1530L760,1533.8L744,1539.2L733.3,1544L728,1546.3L712,1554.9L704.3,1560L696,1565.4L682.7,1576L680,1578.3L666.1,1592L664,1594.2L652.3,1608L648,1613.9L640.9,1624L632,1639.3L631.6,1640L623.3,1656L616.8,1672L616,1673.9L609.9,1688L604.9,1704L600.9,1720L600,1724.1L597.1,1736L593.7,1752L591,1768L588.5,1784L586.4,1800L584.4,1816L584,1819.6L582.2,1832L580.1,1848L578,1864L576.1,1880L574.3,1896L572.8,1912L571.4,1928L570.4,1944L568.6,1960L568.1,1976L568,1980L567.8,1992L567.8,2008L568,2019L568.1,2024L568,2025.2L566.5,2040L565.4,2056L562.5,2072L559.2,2088L554.3,2104L552,2108.8L546.1,2120L536,2134.9L535.2,2136L523.1,2152L520,2155.7L509.4,2168L504,2173.6L494,2184L488,2190.6L479.9,2200L472,2209.3L466.5,2216L456,2229.6L454,2232L441.6,2248L440,2250.2L429.7,2264L424,2272.8L419.2,2280L409.9,2296L408,2299.7L401.2,2312L394,2328L392,2333L387.7,2344L382.4,2360L378.1,2376L376,2385.8L374.4,2392L371.1,2408L368.6,2424L367,2440L366,2456L365.6,2472L365.8,2488L366.7,2504L368.2,2520L370.4,2536L373.3,2552L376,2564.1L376.8,2568L380.6,2584L385.3,2600L390.9,2616L392,2618.9L396.7,2632L403.4,2648L408,2657.8L410.3,2664L416.6,2680L424,2696L424,2696L430.9,2712L438.6,2728L440,2730.7L446.3,2744L455.2,2760L456,2761.6L462.6,2776L470.5,2792L472,2795.1L477.3,2808L484.3,2824L488,2830.9L492.5,2840L499.4,2856L504,2865.1L507.1,2872L513.9,2888L520,2900.4L521.6,2904L530.1,2920L536,2930.3L539.1,2936L549.2,2952L552,2956L560.3,2968L568,2976.3L575.5,2984L584,2993.2L590.8,3000L600,3008.4L609.6,3016L616,3021.3L631.5,3032L632,3032.3L648,3042L660.9,3048L664,3049.5L680,3055.6L696,3060.1L712,3063.2L718.2,3064L728,3065.6L744,3066.8L760,3066.8L776,3065.6L786.4,3064Z","label":[785.1,2431.1]},"1:III":{"path":"M2045,2184L2056,2181.7L2072,2177.6L2088,2172.4L2099.4,2168L2104,2166.2L2120,2159L2132.8,2152L2136,2150.3L2152,2140.8L2159,2136L2168,2130L2180.9,2120L2184,2117.8L2200,2104.5L2200.6,2104L2216,2089.1L2217,2088L2231.3,2072L2232,2071.3L2245,2056L2248,2051.6L2256.4,2040L2264,2028.1L2266.8,2024L2276.6,2008L2280,2001.7L2285.5,1992L2294,1976L2296,1971.5L2301.6,1960L2308.3,1944L2312,1934.2L2314.4,1928L2319.8,1912L2324.5,1896L2328,1882.3L2328.8,1880L2333.7,1864L2338,1848L2341.7,1832L2344,1820.6L2345.1,1816L2348.5,1800L2351.3,1784L2353.7,1768L2355.6,1752L2357.1,1736L2358.2,1720L2358.9,1704L2359.2,1688L2359.1,1672L2358.5,1656L2357.5,1640L2356,1624L2354,1608L2351.3,1592L2347.9,1576L2344,1561L2343.8,1560L2339.6,1544L2334.5,1528L2328.4,1512L2328,1511.2L2323.6,1496L2318.1,1480L2312,1465L2311.6,1464L2303.8,1448L2296,1434L2294.9,1432L2285.6,1416L2280,1407.4L2275.3,1400L2264,1384.3L2263.8,1384L2252.5,1368L2248,1361.9L2240.3,1352L2232,1342.2L2226.7,1336L2216,1324.3L2212,1320L2200,1308.2L2195.4,1304L2184,1293.3L2177.9,1288L2168,1279.3L2158.7,1272L2152,1267.1L2136,1256.6L2134.9,1256L2120,1246L2109.4,1240L2104,1237L2088,1229.4L2073.9,1224L2072,1223.1L2056,1216.7L2040,1211.6L2025.2,1208L2024,1207.7L2008,1204.3L1992,1202L1976,1200.7L1960,1200.2L1944,1200.6L1928,1201.9L1912,1204L1896,1207L1891.8,1208L1880,1210.7L1864,1215.2L1848,1221L1840.9,1224L1832,1227L1816,1233.3L1802.1,1240L1800,1241L1784,1249.6L1773.8,1256L1768,1259.5L1752,1270.1L1749.4,1272L1736,1280.6L1725.6,1288L1720,1292.1L1705,1304L1704,1304.8L1688,1318.4L1686.3,1320L1672,1332.7L1668.4,1336L1656,1348.1L1652.2,1352L1640,1364.9L1637.2,1368L1624,1383.3L1623.4,1384L1610.3,1400L1608,1403L1598.7,1416L1592,1426.9L1588.4,1432L1578.4,1448L1576,1452.2L1569.6,1464L1562.1,1480L1560,1485L1554.4,1496L1547.5,1512L1544,1521.9L1541.6,1528L1536.4,1544L1532.2,1560L1528.9,1576L1528,1581.5L1526.1,1592L1523.9,1608L1522.4,1624L1521.4,1640L1521,1656L1521.1,1672L1521.8,1688L1523,1704L1524.7,1720L1526.9,1736L1528,1742.5L1529.4,1752L1532.2,1768L1535.6,1784L1539.5,1800L1544,1815.9L1544,1816L1548.4,1832L1553.5,1848L1559.2,1864L1560,1866L1563.9,1880L1568.9,1896L1574.6,1912L1576,1915.8L1580.6,1928L1587.6,1944L1592,1952.7L1595.4,1960L1603.4,1976L1608,1984L1612.4,1992L1623.3,2008L1624,2009.1L1633.1,2024L1640,2033.4L1645,2040L1656,2053.6L1657.9,2056L1672,2071.7L1672.3,2072L1688,2086L1690.3,2088L1704,2101L1707.6,2104L1720,2113.9L1728.8,2120L1736,2124.9L1752,2134.6L1754.6,2136L1768,2144.3L1783,2152L1784,2152.5L1800,2160.5L1816,2167L1818.9,2168L1832,2173L1848,2178.1L1864,2182.2L1872.7,2184L1880,2185.7L1896,2188.6L1912,2190.8L1928,2192.3L1944,2193.2L1960,2193.5L1976,2193.2L1992,2192.3L2008,2190.7L2024,2188.4L2040,2185.2L2045,2184Z","label":[1938.3,1702.7]},"1:VII":{"path":"M1282.7,4312L1288,4310.2L1304,4303.5L1317.7,4296L1320,4294.8L1336,4285L1342.8,4280L1352,4273.5L1363.6,4264L1368,4260L1380.1,4248L1384,4243.8L1394.3,4232L1400,4224.6L1406.5,4216L1416,4203.9L1419.1,4200L1428.8,4184L1432,4178.7L1438.8,4168L1446.6,4152L1448,4148.9L1454.2,4136L1460.9,4120L1464,4112L1467.5,4104L1473.7,4088L1479,4072L1480,4068.9L1484.8,4056L1490.1,4040L1494.8,4024L1496,4019.8L1499.9,4008L1504.7,3992L1508.8,3976L1512,3962L1512.5,3960L1516.2,3944L1519.1,3928L1521.4,3912L1523,3896L1524,3880L1524.4,3864L1524.3,3848L1523.4,3832L1521.9,3816L1519.7,3800L1516.7,3784L1513.1,3768L1512,3763.7L1509.3,3752L1505.4,3736L1501.6,3720L1498.5,3704L1496,3688L1496,3686.5L1495.8,3672L1496,3667L1496.6,3656L1499.1,3640L1502.8,3624L1507.9,3608L1512,3594.6L1512.9,3592L1518.7,3576L1524.1,3560L1528,3547.9L1529.4,3544L1535,3528L1539.9,3512L1544,3496.2L1544.1,3496L1549,3480L1553.3,3464L1557,3448L1560,3433.3L1560.3,3432L1563.8,3416L1566.8,3400L1569.2,3384L1571,3368L1572.3,3352L1573,3336L1573.1,3320L1572.5,3304L1571.2,3288L1569.1,3272L1566,3256L1561.8,3240L1560,3234.5L1556.9,3224L1551,3208L1544,3193.2L1543.5,3192L1535.3,3176L1528,3164.4L1525.3,3160L1513.5,3144L1512,3142.1L1500.3,3128L1496,3123.2L1485,3112L1480,3107.2L1467.2,3096L1464,3093.2L1448,3081.1L1446.4,3080L1432,3069.2L1423.9,3064L1416,3058.1L1400.4,3048L1400,3047.7L1384,3035.6L1378.6,3032L1368,3020.5L1363.5,3016L1357.7,3000L1358.9,2984L1366.6,2968L1368,2965.9L1375.8,2952L1383.5,2936L1384,2935.3L1392.7,2920L1399.4,2904L1400,2902.5L1406.1,2888L1410.1,2872L1413.7,2856L1415.7,2840L1416,2826.3L1416.1,2824L1416,2823.3L1414.9,2808L1412.1,2792L1407.5,2776L1400.9,2760L1400,2758.2L1392.3,2744L1384,2732L1381,2728L1368,2713.7L1366.3,2712L1352,2699.9L1346.4,2696L1336,2689.3L1320,2681.2L1316.8,2680L1304,2675.2L1288,2671L1272,2668.6L1256,2667.8L1240,2668.5L1224,2670.9L1208,2675.1L1195,2680L1192,2681.1L1176,2691.7L1173.8,2696L1165.7,2712L1160,2720.3L1156.1,2728L1147.8,2744L1144,2751.5L1140,2760L1132.6,2776L1128,2786.1L1125.6,2792L1118.7,2808L1112.4,2824L1112,2824.9L1106.3,2840L1102,2856L1101.7,2872L1106.8,2888L1112,2899.4L1114.2,2904L1122.4,2920L1128,2928.4L1133.4,2936L1144,2949.6L1146.1,2952L1160,2967.2L1160.9,2968L1176,2983.3L1176.8,2984L1188.7,3000L1192,3006.8L1196.9,3016L1196.9,3032L1192,3041.4L1189.1,3048L1176.5,3064L1176,3064.5L1161.5,3080L1160,3081.3L1144.7,3096L1144,3096.6L1129,3112L1128,3113L1114,3128L1112,3130.2L1100.1,3144L1096,3148.9L1087,3160L1080,3169.8L1075.6,3176L1065.4,3192L1064,3194.4L1055.7,3208L1048,3223.2L1047.6,3224L1039.8,3240L1033.6,3256L1032,3260.9L1027.9,3272L1022.9,3288L1019,3304L1016,3319.9L1016,3320L1013,3336L1010.9,3352L1009.4,3368L1008.5,3384L1008.2,3400L1008.3,3416L1009,3432L1010.1,3448L1011.8,3464L1014,3480L1016,3491.9L1016.6,3496L1018.2,3512L1020.7,3528L1023.3,3544L1025.8,3560L1027.4,3576L1028.5,3592L1028.4,3608L1026.5,3624L1023.1,3640L1018.4,3656L1016,3662.3L1011.9,3672L1004.5,3688L1000,3697.7L996.8,3704L988.9,3720L984,3730.7L981.5,3736L974.4,3752L968.5,3768L968,3769.5L962.3,3784L957,3800L952.9,3816L952,3820.3L949.1,3832L945.9,3848L943.5,3864L941.8,3880L940.8,3896L940.2,3912L940.2,3928L940.6,3944L941.5,3960L942.7,3976L944.3,3992L946.4,4008L948.8,4024L951.7,4040L952,4041.2L954.5,4056L957.6,4072L961.2,4088L965.6,4104L968,4111.7L970.3,4120L975.2,4136L981.1,4152L984,4158.6L987.7,4168L995.1,4184L1000,4192.9L1003.7,4200L1014.6,4216L1016,4218L1025.5,4232L1032,4240.1L1038.5,4248L1048,4258.1L1054,4264L1064,4272.7L1073.8,4280L1080,4284.8L1096,4295.1L1097.7,4296L1112,4304L1128,4310.8L1131.7,4312L1144,4316.1L1160,4320L1176,4322.7L1192,4324.1L1208,4324.6L1224,4324L1240,4322.4L1256,4319.7L1272,4315.6L1282.7,4312Z","label":[1245.3,3658.2]},"1:VIII":{"path":"M2409,2776L2421,2760L2424,2754.9L2430.4,2744L2438.8,2728L2440,2725.3L2445.9,2712L2451.3,2696L2455.2,2680L2456,2674.9L2458,2664L2459.6,2648L2459.8,2632L2458.8,2616L2456.4,2600L2456,2598.2L2453,2584L2448.2,2568L2441.7,2552L2440,2548.6L2433.9,2536L2424,2520.3L2423.8,2520L2412,2504L2408,2499.4L2397.4,2488L2392,2482.8L2379.2,2472L2376,2469.4L2360,2458.4L2355.9,2456L2344,2449.1L2328,2441.8L2323.1,2440L2312,2435.7L2296,2431L2280,2427.6L2264,2425.5L2248,2424.5L2232,2424.5L2216,2425.6L2200,2427.7L2184,2431.1L2168,2435.8L2157.1,2440L2152,2444.3L2147.2,2456L2152,2469.2L2152.8,2472L2157.8,2488L2163.2,2504L2168,2517.6L2168.8,2520L2175.6,2536L2182.2,2552L2184,2555.7L2189.7,2568L2197.9,2584L2200,2587.7L2207,2600L2216,2614.9L2216.7,2616L2227.7,2632L2232,2637.9L2239.8,2648L2248,2658.2L2253,2664L2264,2676.4L2267.5,2680L2280,2693L2283.3,2696L2296,2707.9L2300.9,2712L2312,2722.1L2319.8,2728L2328,2735L2339.8,2744L2344,2748L2360,2759.9L2360.2,2760L2376,2772.8L2380.9,2776L2392,2785.5L2408,2777.2L2409,2776ZM2242.2,4008L2248,4007.4L2264,4004.8L2280,4000.9L2296,3995.5L2304.2,3992L2312,3989.1L2328,3981.8L2338.1,3976L2344,3972.4L2360,3960.6L2360.7,3960L2376,3946.6L2378.7,3944L2392,3930.2L2394,3928L2407.9,3912L2408,3911.9L2418.9,3896L2424,3887.9L2428.9,3880L2437.6,3864L2440,3858.4L2445.2,3848L2452.3,3832L2456,3822.8L2458.9,3816L2465.5,3800L2471.6,3784L2472,3783L2478.2,3768L2484.8,3752L2488,3743.9L2491.6,3736L2498.3,3720L2504,3705.1L2504.5,3704L2511.3,3688L2517.4,3672L2520,3665.2L2523.4,3656L2528.6,3640L2532.9,3624L2536,3611.4L2537.2,3608L2542.5,3592L2547.4,3576L2551.3,3560L2552,3557.1L2555.5,3544L2559.2,3528L2562.5,3512L2565.5,3496L2568,3481.4L2568.3,3480L2571.5,3464L2574.6,3448L2577.5,3432L2580.2,3416L2582.8,3400L2584,3391.3L2585.3,3384L2587.7,3368L2589.6,3352L2591.2,3336L2592.3,3320L2593,3304L2593.2,3288L2593,3272L2592.2,3256L2590.9,3240L2588.9,3224L2586.2,3208L2584,3198L2582.8,3192L2579,3176L2574,3160L2568,3144.1L2568,3144L2561.8,3128L2554.1,3112L2552,3108.1L2546.1,3096L2536.5,3080L2536,3079.2L2526.1,3064L2520,3055.9L2513.9,3048L2504,3036.3L2500.2,3032L2488,3019.2L2484.7,3016L2472,3004.2L2467.1,3000L2456,2990.9L2446.5,2984L2440,2978.9L2424,2968L2424,2968L2408,2957.5L2398,2952L2392,2948.3L2376,2950.2L2373.7,2952L2360,2960L2347.5,2968L2344,2969.7L2328,2979.7L2321.3,2984L2312,2988.6L2296,2997.6L2291.9,3000L2280,3006L2264,3014.7L2261.7,3016L2248,3022.9L2232,3031.1L2230.4,3032L2216,3039.2L2200,3047.2L2198.4,3048L2184,3055L2168,3062.7L2165.4,3064L2152,3070.5L2136,3078.2L2132.3,3080L2120,3086.1L2104,3094.2L2100.2,3096L2088,3102.7L2072,3111.5L2071.1,3112L2056,3121.4L2045.6,3128L2040,3132.3L2024.9,3144L2024,3144.9L2008.2,3160L2008,3160.2L1994.7,3176L1992,3180.1L1983.8,3192L1976.1,3208L1976,3208.4L1969.8,3224L1964.4,3240L1960,3253.1L1958.8,3256L1953.1,3272L1947.3,3288L1944,3298.2L1941.8,3304L1935.5,3320L1929,3336L1928,3338.8L1921.1,3352L1913.2,3368L1912,3370.6L1903.4,3384L1896,3397.3L1894.3,3400L1895.7,3416L1896,3418.9L1897.1,3432L1898.6,3448L1900.2,3464L1901.9,3480L1903.6,3496L1905.3,3512L1906.8,3528L1908.1,3544L1909.1,3560L1909.8,3576L1910.2,3592L1910.2,3608L1910.2,3624L1909.8,3640L1909.4,3656L1909.4,3672L1909.3,3688L1909.5,3704L1910.5,3720L1911.8,3736L1912,3737.4L1913.6,3752L1916.2,3768L1919.8,3784L1924.7,3800L1928,3808.8L1930.5,3816L1937.3,3832L1944,3844.1L1946,3848L1955.4,3864L1960,3870.5L1966.7,3880L1976,3891.6L1979.7,3896L1992,3909.6L1994.3,3912L2008,3925.1L2011.2,3928L2024,3938.5L2031.5,3944L2040,3950.5L2054,3960L2056,3961.3L2072,3971.2L2081.2,3976L2088,3979.6L2104,3986.7L2118.9,3992L2120,3992.4L2136,3998.2L2152,4002.5L2168,4005.8L2184,4008L2184.3,4008L2200,4009.5L2216,4009.9L2232,4009.2L2242.2,4008Z","label":[2228.3,3380.9]},"1:X":{"path":"M3266.4,3128L3272,3127.2L3288,3123.8L3304,3119.1L3320,3112.9L3322,3112L3336,3106.4L3352,3098.4L3356.2,3096L3368,3089.7L3383.3,3080L3384,3079.6L3400,3069.2L3407,3064L3416,3056.2L3424.8,3048L3432,3040.9L3440.5,3032L3448,3024.5L3456.2,3016L3464,3006.7L3469.6,3000L3480,2988.3L3483.8,2984L3496,2970.1L3497.8,2968L3511.9,2952L3512,2951.9L3524.7,2936L3528,2931.8L3537.2,2920L3544,2910.9L3548.8,2904L3559.4,2888L3560,2887L3570.7,2872L3576,2863.7L3581.3,2856L3591.1,2840L3592,2838.3L3600.5,2824L3608,2808.8L3608.5,2808L3616.2,2792L3622.5,2776L3624,2771.6L3628,2760L3632.6,2744L3636.2,2728L3638.9,2712L3640,2703.5L3641.2,2696L3642.8,2680L3643.6,2664L3643.6,2648L3642.7,2632L3641.2,2616L3640,2608.4L3638.9,2600L3636,2584L3632.2,2568L3627.2,2552L3624,2543.5L3621.4,2536L3614.8,2520L3608,2506.3L3606.9,2504L3598.7,2488L3592,2476.7L3589.4,2472L3579.6,2456L3576,2450.4L3569.6,2440L3560,2425.2L3559.2,2424L3550.1,2408L3544,2396.8L3541.4,2392L3534,2376L3528.1,2360L3528,2359.6L3524.4,2344L3522.2,2328L3520.9,2312L3520.1,2296L3520.5,2280L3520.5,2264L3520.8,2248L3520.7,2232L3519.7,2216L3517.8,2200L3514.1,2184L3512,2175.3L3510.4,2168L3505.8,2152L3499.7,2136L3496,2127.9L3492.5,2120L3484,2104L3480,2097.7L3474,2088L3464,2074.3L3462.2,2072L3448.7,2056L3448,2055.2L3432.9,2040L3432,2039.1L3416,2025.4L3414.2,2024L3400,2013.5L3391.4,2008L3384,2003.4L3368,1994.8L3361.7,1992L3352,1987.5L3336,1981.5L3320,1977L3315.5,1976L3304,1973.3L3288,1970.8L3272,1969.5L3256,1969.3L3240,1970.4L3224,1972.6L3209,1976L3208,1976.2L3192,1980.8L3176,1987L3165.9,1992L3160,1994.9L3144,2004.5L3139.2,2008L3128,2016.4L3119.3,2024L3112,2031L3103.6,2040L3096,2049.3L3090.9,2056L3080.6,2072L3080,2073.1L3072,2088L3065.4,2104L3064,2108.2L3060,2120L3056,2136L3053.3,2152L3051.8,2168L3051.5,2184L3051.6,2200L3052.5,2216L3054.6,2232L3057.4,2248L3060.5,2264L3064,2279.3L3064.2,2280L3067.2,2296L3068.7,2312L3069.6,2328L3068.1,2344L3065.2,2360L3064,2363.7L3059.8,2376L3052.8,2392L3048,2401.2L3044.4,2408L3035.4,2424L3032,2430.1L3026,2440L3017,2456L3016,2457.9L3008.1,2472L3000.4,2488L3000,2489L2992.7,2504L2986.4,2520L2984,2527.1L2980.5,2536L2975.1,2552L2970.7,2568L2968,2579.4L2966.8,2584L2963.5,2600L2961,2616L2959.1,2632L2957.8,2648L2957,2664L2963.2,2680L2968,2685.6L2975.4,2696L2984,2706.4L2987.6,2712L2999.2,2728L3000,2729L3010,2744L3016,2752.1L3021,2760L3032,2775.8L3032.1,2776L3041.9,2792L3048,2801.7L3051.6,2808L3060.7,2824L3064,2829.9L3069.3,2840L3077.4,2856L3080,2861.3L3085,2872L3092.3,2888L3096,2896.4L3099.3,2904L3106.3,2920L3112,2933.5L3113.1,2936L3119.9,2952L3127.1,2968L3128,2970L3134.4,2984L3142,3000L3144,3004.4L3150,3016L3158.7,3032L3160,3034.7L3167.6,3048L3176,3063.2L3176.6,3064L3187.7,3080L3192,3087.3L3198.5,3096L3208,3110.1L3209.7,3112L3220.9,3128L3224,3131.2L3240,3131L3256,3129.7L3266.4,3128Z","label":[3283,2616.2]},"1:VI":{"path":"M1903.4,3384L1912,3370.6L1913.2,3368L1921.1,3352L1928,3338.8L1929,3336L1935.5,3320L1941.8,3304L1944,3298.2L1947.3,3288L1953.1,3272L1958.8,3256L1960,3253.1L1964.4,3240L1969.8,3224L1976,3208.4L1976.1,3208L1983.8,3192L1992,3180.1L1994.7,3176L2008,3160.2L2008.2,3160L2024,3144.9L2024.9,3144L2040,3132.3L2045.6,3128L2056,3121.4L2071.1,3112L2072,3111.5L2088,3102.7L2100.2,3096L2104,3094.2L2120,3086.1L2132.3,3080L2136,3078.2L2152,3070.5L2165.4,3064L2168,3062.7L2184,3055L2198.4,3048L2200,3047.2L2216,3039.2L2230.4,3032L2232,3031.1L2248,3022.9L2261.7,3016L2264,3014.7L2280,3006L2291.9,3000L2296,2997.6L2312,2988.6L2321.3,2984L2328,2979.7L2344,2969.7L2347.5,2968L2360,2960L2373.7,2952L2376,2949.9L2387.4,2936L2391,2920L2392,2914.6L2394.4,2904L2397.1,2888L2399,2872L2400.2,2856L2400.7,2840L2400.5,2824L2399.7,2808L2397.1,2792L2392,2785.5L2380.9,2776L2376,2772.8L2360.2,2760L2360,2759.9L2344,2748L2339.8,2744L2328,2735L2319.8,2728L2312,2722.1L2300.9,2712L2296,2707.9L2283.3,2696L2280,2693L2267.5,2680L2264,2676.4L2253,2664L2248,2658.2L2239.8,2648L2232,2637.9L2227.7,2632L2216.7,2616L2216,2614.9L2207,2600L2200,2587.7L2197.9,2584L2189.7,2568L2184,2555.7L2182.2,2552L2175.6,2536L2168.8,2520L2168,2517.6L2163.2,2504L2157.8,2488L2152.8,2472L2152,2469.2L2147.2,2456L2136,2444.2L2125.9,2440L2120,2437.8L2104,2432.8L2088,2429.1L2072,2426.3L2056,2424.5L2047.8,2424L2040,2423.4L2024,2423.2L2008,2424L2007.7,2424L1992,2425.4L1976,2427.8L1960,2431.3L1944,2436L1933.4,2440L1928,2441.7L1912,2447.9L1896,2456L1896,2456L1880,2464.9L1869.6,2472L1864,2475.8L1848.7,2488L1848,2488.6L1832,2502.1L1830,2504L1816,2518.6L1814.7,2520L1800.7,2536L1800,2536.9L1788.5,2552L1784,2558.9L1777.8,2568L1768.6,2584L1768,2585.1L1759.7,2600L1752.2,2616L1752,2616.5L1744.8,2632L1738.7,2648L1736,2656.3L1733.1,2664L1727.9,2680L1723.6,2696L1720.1,2712L1720,2712.3L1716.5,2728L1713.7,2744L1711.6,2760L1710.1,2776L1709.1,2792L1708.7,2808L1708.9,2824L1709.6,2840L1710.9,2856L1712.9,2872L1715.4,2888L1718.9,2904L1720,2908.4L1722.6,2920L1727,2936L1732.3,2952L1736,2961.3L1738.3,2968L1744.3,2984L1751.4,3000L1752,3001.3L1758,3016L1765.1,3032L1768,3038.7L1771.7,3048L1777.7,3064L1783.2,3080L1784,3083.1L1786.8,3096L1789,3112L1789.3,3128L1788.1,3144L1785.9,3160L1784,3175.6L1783.9,3176L1781.5,3192L1779.1,3208L1777.2,3224L1776.6,3240L1777.5,3256L1779.6,3272L1783.6,3288L1784,3289.2L1788.8,3304L1796,3320L1800,3326.7L1805.8,3336L1816,3349.3L1818.3,3352L1832,3365.6L1834.8,3368L1848,3378.1L1857.8,3384L1864,3387.6L1880,3394.7L1896,3397L1903.4,3384Z","label":[2034.2,2836.5]},"1:IX":{"path":"M3039,3832L3048,3828.8L3064,3821.5L3073.7,3816L3080,3812.4L3096,3801.3L3097.6,3800L3112,3788L3116.2,3784L3128,3772L3131.6,3768L3144,3752L3144,3752L3154.7,3736L3160,3726.2L3163.4,3720L3170.7,3704L3176,3688.9L3176.4,3688L3181.2,3672L3184.7,3656L3186.9,3640L3188,3624L3188.1,3608L3187.1,3592L3185,3576L3181.6,3560L3177,3544L3176,3541.4L3171.5,3528L3164.7,3512L3160,3502.3L3157.1,3496L3148.2,3480L3144,3473.2L3138.4,3464L3128,3448.2L3127.9,3448L3117.6,3432L3112,3423L3107.8,3416L3102.2,3400L3096.5,3384L3096,3381.5L3093.7,3368L3093.5,3352L3096,3336L3096,3336L3101.5,3320L3108.4,3304L3112,3298.5L3119.3,3288L3128,3275.5L3130.6,3272L3143.7,3256L3144,3255.6L3156.4,3240L3160,3235L3167.2,3224L3176,3210.4L3177.9,3208L3189.4,3192L3192,3187.9L3199.7,3176L3208,3160.8L3208.5,3160L3216.8,3144L3220.5,3128L3209.7,3112L3208,3110.1L3198.5,3096L3192,3087.3L3187.7,3080L3176.6,3064L3176,3063.2L3167.6,3048L3160,3034.7L3158.7,3032L3150,3016L3144,3004.4L3142,3000L3134.4,2984L3128,2970L3127.1,2968L3119.9,2952L3113.1,2936L3112,2933.5L3106.3,2920L3099.3,2904L3096,2896.4L3092.3,2888L3085,2872L3080,2861.3L3077.4,2856L3069.3,2840L3064,2829.9L3060.7,2824L3051.6,2808L3048,2801.7L3041.9,2792L3032.1,2776L3032,2775.8L3021,2760L3016,2752.1L3010,2744L3000,2729L2999.2,2728L2987.6,2712L2984,2706.4L2975.4,2696L2968,2685.6L2961.1,2680L2952,2671.1L2936,2671.9L2920,2673.7L2904,2676.7L2891.3,2680L2888,2680.8L2872,2685.7L2856,2692.2L2848.2,2696L2840,2699.9L2824,2709.1L2819.7,2712L2808,2719.9L2797.8,2728L2792,2732.8L2780,2744L2776,2748.1L2765.2,2760L2760,2766.2L2752.3,2776L2744,2788.6L2741.8,2792L2732.7,2808L2728,2818.2L2725.2,2824L2718.9,2840L2714,2856L2712,2864.6L2710.1,2872L2707.1,2888L2705.1,2904L2703.4,2920L2702.8,2936L2702.9,2952L2703.5,2968L2704.4,2984L2705.4,3000L2706.4,3016L2707,3032L2707.2,3048L2706.6,3064L2704.7,3080L2702.3,3096L2699.1,3112L2696,3125.7L2695.4,3128L2690.9,3144L2686.3,3160L2682,3176L2680,3183.8L2677.7,3192L2673.8,3208L2670.5,3224L2667.8,3240L2665.8,3256L2664.6,3272L2664,3282.6L2663.7,3288L2663.6,3304L2663.7,3320L2664,3328.5L2664.3,3336L2665.2,3352L2666.5,3368L2668.3,3384L2670.4,3400L2673,3416L2676,3432L2679.6,3448L2680,3449.5L2683.4,3464L2687.7,3480L2692.7,3496L2696,3505L2698.3,3512L2704,3528L2710.3,3544L2712,3548.2L2716.5,3560L2722.8,3576L2728,3586.4L2730.6,3592L2736.3,3608L2742.3,3624L2744,3628.4L2748,3640L2754,3656L2760,3670.9L2760.4,3672L2766.8,3688L2774.1,3704L2776,3707.7L2782,3720L2791.2,3736L2792,3737.2L2801.5,3752L2808,3760.7L2813.7,3768L2824,3777.9L2831.1,3784L2840,3792.8L2848.3,3800L2856,3806.1L2870.9,3816L2872,3816.7L2888,3825.5L2904,3832L2904.1,3832L2920,3837.4L2936,3841L2952,3843.3L2968,3844.1L2984,3843.8L3000,3842.1L3016,3839.1L3032,3834.6L3039,3832Z","label":[2935.8,3235.1]},"1:XI":{"path":"M3829.4,4104L3832,4103.5L3848,4099.5L3864,4094.1L3878.4,4088L3880,4087.3L3896,4079.5L3908.2,4072L3912,4069.7L3928,4058.6L3931.3,4056L3944,4045.7L3950.3,4040L3960,4030.6L3966.3,4024L3976,4012.6L3979.8,4008L3991.4,3992L3992,3991L4001.8,3976L4008,3964.2L4010.3,3960L4017.9,3944L4023.9,3928L4024,3927.7L4029.5,3912L4033.9,3896L4037.2,3880L4039.5,3864L4040,3858.9L4041.3,3848L4042.3,3832L4042.7,3816L4042.2,3800L4041,3784L4040,3775.9L4039.2,3768L4037,3752L4034.3,3736L4031,3720L4027.1,3704L4024,3692.6L4022.9,3688L4018.9,3672L4014.7,3656L4010.5,3640L4008,3629.9L4006.7,3624L4003.5,3608L4000.7,3592L3998.5,3576L3996.8,3560L3995.7,3544L3995,3528L3994.7,3512L3994.7,3496L3994.7,3480L3994.5,3464L3993.6,3448L3993,3432L3992,3419.5L3991.8,3416L3990.3,3400L3988.2,3384L3985.5,3368L3981.9,3352L3977.6,3336L3976,3331.3L3972.6,3320L3967.2,3304L3960.6,3288L3960,3286.7L3953.7,3272L3945.3,3256L3944,3253.9L3936.1,3240L3928,3228.2L3925.1,3224L3912.6,3208L3912,3207.3L3898.3,3192L3896,3189.7L3881.1,3176L3880,3175L3864,3162.4L3860.4,3160L3848,3151.7L3833.5,3144L3832,3143.2L3816,3136L3800,3130.6L3789.6,3128L3784,3126.3L3768,3122.8L3752,3120.7L3736,3119.7L3720,3120L3704,3121.4L3688,3124.1L3672.9,3128L3672,3128.2L3656,3132.6L3640,3138.5L3628.3,3144L3624,3146.1L3608,3155.3L3601.2,3160L3592,3166.4L3580.3,3176L3576,3179.4L3561.8,3192L3560,3193.8L3547.1,3208L3544,3211.7L3534.3,3224L3528,3233.2L3523.3,3240L3513.7,3256L3512,3259.3L3504.9,3272L3497.4,3288L3496,3291.3L3490.1,3304L3483.8,3320L3480,3330.7L3477.9,3336L3472.1,3352L3467,3368L3464,3378.5L3462.2,3384L3457.4,3400L3453.3,3416L3449.7,3432L3448,3440.8L3446.4,3448L3443.4,3464L3441.2,3480L3439.7,3496L3438.9,3512L3438.8,3528L3439.5,3544L3440.9,3560L3443.2,3576L3446.2,3592L3448,3599.6L3449.7,3608L3453.5,3624L3457.8,3640L3462.6,3656L3464,3660.7L3466.9,3672L3471.2,3688L3474.9,3704L3478.3,3720L3480,3729.3L3481,3736L3483.1,3752L3484.8,3768L3486.4,3784L3487.9,3800L3489.5,3816L3491.4,3832L3493.6,3848L3496,3858.1L3497.1,3864L3499.8,3880L3503.2,3896L3508.1,3912L3512,3923.5L3513.4,3928L3519.3,3944L3526.7,3960L3528,3962.4L3534.9,3976L3544,3990.5L3544.9,3992L3556,4008L3560,4012.9L3569.2,4024L3576,4031.4L3584.6,4040L3592,4046.8L3603.1,4056L3608,4059.9L3624,4071L3625.7,4072L3640,4080.8L3654.9,4088L3656,4088.5L3672,4095.3L3688,4100.5L3702.6,4104L3704,4104.4L3720,4108.1L3736,4110.5L3752,4111.9L3768,4112.2L3784,4111.6L3800,4110L3816,4107.3L3829.4,4104Z","label":[3730.9,3617]},"1:V":{"path":"M443.5,3960L456,3956.9L472,3951.7L488,3944.8L489.7,3944L504,3937.3L519.8,3928L520,3927.9L536,3918.5L545.3,3912L552,3907.2L565.7,3896L568,3894.2L584,3880.6L584.7,3880L600,3865.7L601.8,3864L616,3848.1L616.1,3848L629.2,3832L632,3828.4L641.6,3816L648,3807.6L653.3,3800L662.6,3784L664,3781.7L674.3,3768L680,3758.7L683.9,3752L693,3736L696,3730L701.8,3720L710,3704L712,3699.9L718.4,3688L726.1,3672L728,3667.6L733.5,3656L740.1,3640L744,3628.9L745.9,3624L751.7,3608L756.7,3592L760,3580L761.2,3576L765.5,3560L769.1,3544L772.2,3528L774.8,3512L776,3502.9L777.3,3496L779.7,3480L781.7,3464L783,3448L783.9,3432L784.3,3416L784.1,3400L783.4,3384L782.1,3368L780.1,3352L777.3,3336L776,3330.1L774.1,3320L770.2,3304L765.3,3288L760,3274.5L759.1,3272L752.5,3256L744.1,3240L744,3239.8L735.5,3224L728,3212.5L725.1,3208L713,3192L712,3190.7L699.6,3176L696,3172.1L684.1,3160L680,3156L666.5,3144L664,3141.8L648,3129.6L645.6,3128L632,3118.7L620.1,3112L616,3109.6L600,3101.5L586.3,3096L584,3094.9L568,3088.5L552,3083.5L537.7,3080L536,3079.5L520,3076.1L504,3073.6L488,3072L472,3071.2L456,3071.1L440,3071.8L424,3073.3L408,3075.6L392,3078.8L387.4,3080L376,3082.5L360,3086.8L344,3092.2L334.6,3096L328,3098.4L312,3105.4L299.3,3112L296,3113.4L280,3121.3L268.2,3128L264,3130.4L248,3140.7L243.4,3144L232,3151.8L221.2,3160L216,3163.7L200.4,3176L200,3176.3L184,3189.8L181.6,3192L168,3205.3L165.3,3208L152,3222L150.2,3224L136.2,3240L136,3240.2L123.1,3256L120,3260.2L111.5,3272L104,3283.8L101.3,3288L92.3,3304L88,3312.8L83.9,3320L76.1,3336L72,3346.2L69.5,3352L63.3,3368L58.5,3384L56,3394.5L54.5,3400L50.8,3416L48.1,3432L46,3448L44.7,3464L44,3480L43.8,3496L44.2,3512L45,3528L46.3,3544L48.1,3560L50.3,3576L52.9,3592L55.9,3608L56,3608.3L58.8,3624L62,3640L65.6,3656L69.7,3672L72,3680.4L73.8,3688L77.9,3704L82.6,3720L88,3735.9L88,3736L93,3752L98.9,3768L104,3779.5L105.7,3784L113,3800L120,3813.4L121.3,3816L130.3,3832L136,3840.7L140.7,3848L152,3861.8L153.9,3864L167.3,3880L168,3880.8L183,3896L184,3896.9L200,3910.1L202.6,3912L216,3921.9L225.8,3928L232,3932.1L248,3940.9L254.7,3944L264,3948.2L280,3954.2L296,3958.7L301.8,3960L312,3962.8L328,3966L344,3968.1L360,3969.2L376,3969.4L392,3968.7L408,3967.1L424,3964.6L440,3961L443.5,3960Z","label":[408,3506.2]},"L:4":{"path":"M6568.5,680L6584,676.6L6600,672.1L6616,666.1L6620.9,664L6632,659.5L6648,651.5L6654,648L6664,643L6680,633.4L6682,632L6696,622.3L6704,616L6712,609.6L6722.7,600L6728,595.1L6739.2,584L6744,578.9L6753.8,568L6760,560.4L6766.8,552L6776,539L6778.1,536L6788.3,520L6792,513.2L6797.4,504L6805.5,488L6808,482.1L6812.8,472L6819,456L6824,440.1L6824,440L6828.6,424L6832.2,408L6834.9,392L6836.8,376L6837.9,360L6838.3,344L6838,328L6837,312L6835.1,296L6832.3,280L6828.5,264L6824,249.8L6823.5,248L6818,232L6811,216L6808,210.2L6803.1,200L6793.6,184L6792,181.7L6783.4,168L6776,158.1L6771.2,152L6760,139.3L6756.9,136L6744,123.3L6740.3,120L6728,109.6L6720.6,104L6712,97.7L6696.5,88L6696,87.7L6680,78.6L6665.2,72L6664,71.4L6648,64.6L6632,59.3L6619.2,56L6616,55.1L6600,51.5L6584,49L6568,47.3L6552,46.5L6536,46.4L6520,47L6504,48.4L6488,50.6L6472,53.7L6462.6,56L6456,57.5L6440,61.9L6424,67.6L6413.8,72L6408,74.1L6392,80.9L6378.4,88L6376,89.2L6360,98.5L6351.8,104L6344,109.2L6329.9,120L6328,121.5L6312,135.2L6311.1,136L6296,150.8L6294.8,152L6280.6,168L6280,168.8L6267.9,184L6264,189.7L6256.8,200L6248,215.2L6247.5,216L6238.8,232L6232,247.7L6231.9,248L6225.2,264L6220,280L6216,295.6L6215.9,296L6212.4,312L6209.9,328L6208.1,344L6207,360L6206.7,376L6207,392L6208,408L6209.8,424L6212.5,440L6216,455.6L6216.1,456L6220.1,472L6225.3,488L6231.9,504L6232,504.3L6238.7,520L6247.3,536L6248,537.2L6256.4,552L6264,563L6267.4,568L6280,583.9L6280.1,584L6294.3,600L6296,601.7L6311.1,616L6312,616.9L6328,630L6330.7,632L6344,641.4L6355.2,648L6360,651L6376,659.5L6386.5,664L6392,666.4L6408,672.2L6424,676.7L6439.7,680L6440,680.1L6456,683.5L6472,685.8L6488,687.2L6504,687.6L6520,687.2L6536,685.8L6552,683.5L6568,680.1L6568.5,680Z","label":[6510.9,358.1]},"L:5":{"path":"M5203.7,1480L5208,1478.5L5224,1471.5L5240,1464.5L5241,1464L5256,1457.2L5272,1449.6L5275,1448L5288,1441.6L5304,1433.2L5306.2,1432L5320,1424.8L5336,1416.3L5336.5,1416L5352,1407.5L5365.7,1400L5368,1398.7L5384,1389.5L5394,1384L5400,1380.3L5416,1370.8L5420.9,1368L5432,1361.1L5447.3,1352L5448,1351.6L5464,1342L5475,1336L5480,1332.7L5496,1323.3L5502,1320L5512,1305.2L5513,1304L5521,1288L5528,1273.8L5529,1272L5537.1,1256L5544,1240.2L5544.1,1240L5551.5,1224L5558.2,1208L5560,1203.2L5565,1192L5571.4,1176L5576,1163.7L5577.7,1160L5584.4,1144L5590.2,1128L5592,1122.4L5595.5,1112L5600.3,1096L5604.3,1080L5607.7,1064L5608,1062.5L5611.5,1048L5614.6,1032L5617,1016L5618.7,1000L5619.9,984L5620.5,968L5620.7,952L5620.4,936L5619.7,920L5618.4,904L5616.7,888L5614.5,872L5611.8,856L5608.5,840L5608,838.1L5605.6,824L5602.3,808L5598.5,792L5594,776L5592,769.5L5589.1,760L5583.6,744L5577.1,728L5576,725.6L5570.4,712L5562.5,696L5560,691.4L5554.3,680L5545.1,664L5544,662.2L5536.5,648L5528,633.7L5527.1,632L5517.8,616L5512,607.4L5507.2,600L5496,584.1L5495.9,584L5482.6,568L5480,564.9L5469.3,552L5464,546.8L5448,547.4L5432,550.5L5424.9,552L5416,553.4L5400,556.3L5384,559.2L5368,562L5352,564.8L5336,567.6L5334,568L5320,570.1L5304,572.5L5288,574.8L5272,577.1L5256,579.2L5240,581.2L5224,583.1L5216.3,584L5208,584.9L5192,586.5L5176,587.9L5160,589.2L5144,590.4L5128,591.5L5112,592.5L5096,593.3L5080,594.1L5064,594.7L5048,595.2L5032,595.6L5016,595.8L5000,595.9L4984,595.9L4968,595.8L4952,595.5L4936,595L4920,594.4L4911.4,600L4904,609.4L4899.8,616L4890.8,632L4888,637.6L4882.2,648L4874.5,664L4872,669.8L4867.3,680L4860.8,696L4856,709.4L4855,712L4849.1,728L4844.1,744L4840,759.1L4839.7,760L4834.6,776L4830.4,792L4826.8,808L4824,822.6L4823.7,824L4820.8,840L4818.4,856L4816.5,872L4815,888L4813.9,904L4813.2,920L4812.8,936L4812.8,952L4813.2,968L4813.9,984L4815,1000L4816.5,1016L4818.5,1032L4820.9,1048L4824,1063.8L4824,1064L4826.7,1080L4830,1096L4833.8,1112L4838.3,1128L4840,1133.6L4842.8,1144L4847.9,1160L4853.8,1176L4856,1181.5L4859.7,1192L4866.4,1208L4872,1219.5L4873.9,1224L4881.3,1240L4888,1252L4890.2,1256L4899.8,1272L4904,1278.3L4909.9,1288L4920,1303.2L4920.5,1304L4931.8,1320L4936,1325.1L4945,1336L4952,1344.3L4958.6,1352L4968,1362.6L4972.9,1368L4984,1378.9L4989.5,1384L5000,1393.7L5007.3,1400L5016,1407.8L5026,1416L5032,1421.2L5045.9,1432L5048,1433.5L5064,1444.2L5070.5,1448L5080,1454.2L5096,1463L5098,1464L5112,1470.8L5128,1477.1L5136.9,1480L5144,1483.1L5160,1489L5176,1490.9L5192,1485.4L5203.7,1480Z","label":[5201.4,954.2]},"L:18":{"path":"M7241.6,1304L7256,1301.3L7272,1297.2L7288,1292.3L7300.2,1288L7304,1286.1L7320,1278.2L7322.5,1272L7324.2,1256L7320,1243.8L7318.4,1240L7313.1,1224L7305.3,1208L7304,1205.8L7296.3,1192L7288,1180.2L7284.9,1176L7272,1161L7271.1,1160L7256,1145.7L7253.9,1144L7240,1133.4L7231.4,1128L7224,1123.4L7208,1115.5L7198.9,1112L7192,1109.3L7176,1104.4L7160,1101.2L7144,1099.4L7128,1098.8L7112,1099.5L7096,1101.5L7080,1104.9L7064,1109.9L7058.9,1112L7048,1116.2L7032,1124.3L7026,1128L7016,1134.2L7003.1,1144L7000,1146.4L6985.4,1160L6984,1161.4L6971.1,1176L6968,1180L6959.3,1192L6952,1205.7L6950.7,1208L6952,1210.5L6968,1223.1L6968.9,1224L6984,1233L6994.3,1240L7000,1242.8L7016,1251.8L7022.9,1256L7032,1260.2L7048,1268L7056,1272L7064,1275.3L7080,1281.7L7096,1287.9L7096.3,1288L7112,1292.8L7128,1297L7144,1300.7L7160,1303.6L7163.1,1304L7176,1305.5L7192,1306.5L7208,1306.7L7224,1306L7240,1304.2L7241.6,1304ZM7020.5,2408L7032,2406.8L7048,2405.2L7064,2403.8L7080,2402.6L7096,2401.5L7112,2400.6L7128,2399.7L7144,2399L7160,2398.4L7176,2397.8L7192,2397.3L7208,2396.8L7224,2396.4L7240,2395.9L7256,2395.5L7272,2395L7288,2394.5L7304,2394L7320,2393.4L7336,2392.8L7349.5,2392L7352,2391.8L7368,2391L7384,2389.5L7395.7,2376L7400,2367.3L7403.3,2360L7409.4,2344L7414.2,2328L7416,2320.4L7418.5,2312L7422.4,2296L7425.6,2280L7428,2264L7429.8,2248L7431.3,2232L7432,2219.2L7432.2,2216L7433,2200L7433.5,2184L7434.1,2168L7434.9,2152L7435.8,2136L7437.1,2120L7439,2104L7441.4,2088L7444.3,2072L7447.6,2056L7448,2054.2L7452.3,2040L7457.1,2024L7461.8,2008L7464,2000L7466.3,1992L7470.6,1976L7474.3,1960L7477.4,1944L7479.8,1928L7480,1926.2L7482.2,1912L7484,1896L7484.9,1880L7485.1,1864L7484.6,1848L7483.3,1832L7481.2,1816L7480,1809.1L7476.4,1800L7464,1789.7L7448,1795.6L7432,1794.1L7416,1794.6L7400,1796.5L7384,1797.4L7368,1797.1L7352,1798.3L7336,1798.5L7320,1799.6L7310.5,1800L7304,1800.2L7288,1800.8L7272,1801.3L7256,1801.7L7240,1802.2L7224,1802.6L7208,1803.1L7192,1803.4L7176,1803.8L7160,1804.1L7144,1804.4L7128,1804.6L7112,1804.6L7096,1804.5L7080,1804.3L7064,1803.8L7048,1803L7032,1802L7016,1800.6L7009.7,1800L7000,1798.6L6984,1795.7L6968,1792.1L6952,1787.8L6939.5,1784L6936,1782.3L6920,1774L6910.8,1768L6904,1752L6906.3,1736L6916.6,1720L6920,1716.3L6930.5,1704L6936,1699L6946.2,1688L6952,1681.6L6958.9,1672L6966.9,1656L6968,1650.5L6969.5,1640L6969,1624L6968,1620.4L6963.9,1608L6955.5,1592L6952,1587.3L6942.2,1576L6936,1569.6L6925.3,1560L6920,1555.6L6904.3,1544L6904,1543.8L6888,1534.1L6877.4,1528L6872,1524.8L6856,1516.2L6840,1525.5L6839,1528L6832.8,1544L6826.1,1560L6824,1563.1L6818.6,1576L6812,1592L6808,1601.1L6805,1608L6798,1624L6792,1638.2L6791.2,1640L6784.3,1656L6778.1,1672L6776,1675.7L6770.5,1688L6764.8,1704L6760,1714.3L6757.5,1720L6755.2,1736L6754.8,1752L6754.6,1768L6754.3,1784L6754.3,1800L6754.4,1816L6754.4,1832L6754.4,1848L6754.1,1864L6753.8,1880L6753.3,1896L6752.5,1912L6751.5,1928L6750.2,1944L6748.7,1960L6747,1976L6745.2,1992L6744,2001.6L6743,2008L6740.5,2024L6738.1,2040L6735.8,2056L6733.8,2072L6732.3,2088L6731.2,2104L6730.6,2120L6730.4,2136L6730.7,2152L6731.6,2168L6733.1,2184L6735.2,2200L6738,2216L6741.8,2232L6744,2235.2L6755.5,2248L6760,2250.6L6776,2261.2L6779.6,2264L6792,2271.8L6804.1,2280L6808,2282.2L6824,2292.7L6828.2,2296L6840,2303.5L6852.5,2312L6856,2314.1L6872,2324.8L6876.4,2328L6888,2335.8L6899.4,2344L6904,2347.1L6920,2358.5L6922,2360L6936,2370.3L6943.7,2376L6952,2382.2L6964.9,2392L6968,2394.5L6984,2406.9L6989.6,2408L7000,2410.8L7016,2408.6L7020.5,2408Z","label":[7098.2,1941.1]},"L:19":{"path":"M7241.4,3464L7256,3456.9L7270.3,3448L7272,3447L7288,3435.4L7292.1,3432L7304,3421.5L7309.6,3416L7320,3404.8L7324.1,3400L7336,3384.7L7336.5,3384L7347.9,3368L7352,3360.8L7357.2,3352L7365.6,3336L7368,3330.4L7372.8,3320L7379.2,3304L7384,3289L7384.3,3288L7389.4,3272L7393.7,3256L7397.2,3240L7400,3224.5L7400.1,3224L7403.2,3208L7405.7,3192L7407.8,3176L7409.7,3160L7411.1,3144L7412.5,3128L7413.6,3112L7414.3,3096L7414.9,3080L7415.4,3064L7415.6,3048L7415.8,3032L7416,3023.8L7416.2,3016L7416.3,3000L7416.4,2984L7416.6,2968L7416.9,2952L7417.3,2936L7418,2920L7418.9,2904L7420,2888L7421.2,2872L7422.6,2856L7423.9,2840L7425.3,2824L7426.4,2808L7427.3,2792L7427.8,2776L7428.1,2760L7428.1,2744L7427.5,2728L7426.7,2712L7425.4,2696L7423.8,2680L7421.8,2664L7419.5,2648L7416.9,2632L7416,2626.5L7414.6,2616L7412.5,2600L7410.5,2584L7408.6,2568L7406.8,2552L7405.3,2536L7403.9,2520L7402.6,2504L7401.4,2488L7400.1,2472L7400,2471.4L7398.7,2456L7397.3,2440L7395.4,2424L7393.1,2408L7386.8,2392L7384,2389.5L7368,2391L7352,2391.8L7349.5,2392L7336,2392.8L7320,2393.4L7304,2394L7288,2394.5L7272,2395L7256,2395.5L7240,2395.9L7224,2396.4L7208,2396.8L7192,2397.3L7176,2397.8L7160,2398.4L7144,2399L7128,2399.7L7112,2400.6L7096,2401.5L7080,2402.6L7064,2403.8L7048,2405.2L7032,2406.8L7020.5,2408L7016,2408.6L7000,2412.3L6994.1,2424L6998.7,2440L7000,2444.6L7002.9,2456L7006.5,2472L7009.6,2488L7011.9,2504L7013.3,2520L7014.1,2536L7013.9,2552L7012.4,2568L7010,2584L7006.7,2600L7002.3,2616L7000,2623.1L6997,2632L6990.7,2648L6984.2,2664L6984,2664.4L6977.5,2680L6970.8,2696L6968,2703.3L6964.3,2712L6958.7,2728L6954.1,2744L6952,2753.5L6950.4,2760L6948,2776L6946.5,2792L6945.9,2808L6945.5,2824L6945.9,2840L6946,2856L6946.2,2872L6945.9,2888L6944.7,2904L6943.4,2920L6941.3,2936L6938.5,2952L6936,2965.3L6935.4,2968L6930.6,2984L6925.8,3000L6921.1,3016L6920,3019.8L6915.6,3032L6910.2,3048L6906.1,3064L6904,3074.9L6902.7,3080L6900.9,3096L6903.7,3112L6904,3112.9L6908.4,3128L6916.7,3144L6920,3148.1L6928,3160L6936,3168.7L6941.7,3176L6952,3186.9L6956.2,3192L6968,3204.3L6971.1,3208L6984,3221.4L6986.3,3224L7000,3239L7000.8,3240L7015.3,3256L7016,3256.8L7029.4,3272L7032,3275L7043,3288L7048,3294.2L7056,3304L7064,3313.9L7069.1,3320L7080,3334.3L7081.4,3336L7093.9,3352L7096,3355.1L7106,3368L7112,3376.5L7118.3,3384L7128,3397.7L7130.1,3400L7141.5,3416L7144,3420.2L7152.8,3432L7160,3443.7L7163.7,3448L7174.9,3464L7176,3465.8L7192,3478.9L7208,3475.6L7224,3471L7240,3464.6L7241.4,3464Z","label":[7130,2776.3]},"L:21":{"path":"M7310.5,1800L7320,1799.6L7336,1798.5L7352,1798.3L7368,1797.1L7384,1797.4L7400,1796.5L7416,1794.6L7432,1794.1L7448,1795.6L7464,1789.7L7473.1,1784L7480,1771.2L7480.6,1768L7482.6,1752L7483.8,1736L7484.2,1720L7483.9,1704L7482.7,1688L7480.9,1672L7480,1666.6L7478.5,1656L7475.6,1640L7471.7,1624L7466.7,1608L7464,1600.9L7461.5,1592L7456.3,1576L7449.8,1560L7448,1556L7442.4,1544L7433.5,1528L7432,1525.6L7424.3,1512L7416,1499L7414.3,1496L7405.2,1480L7400,1471.2L7396,1464L7387.5,1448L7384,1441.3L7379.2,1432L7372.3,1416L7368,1405L7366.3,1400L7361.4,1384L7356.2,1368L7352.2,1352L7352,1351.4L7348.3,1336L7343.7,1320L7339.1,1304L7336,1295.3L7328.1,1288L7320,1278.2L7304,1286.1L7300.2,1288L7288,1292.3L7272,1297.2L7256,1301.3L7241.6,1304L7240,1304.2L7224,1306L7208,1306.7L7192,1306.5L7176,1305.5L7163.1,1304L7160,1303.6L7144,1300.7L7128,1297L7112,1292.8L7096.3,1288L7096,1287.9L7080,1281.7L7064,1275.3L7056,1272L7048,1268L7032,1260.2L7022.9,1256L7016,1251.8L7000,1242.8L6994.3,1240L6984,1233L6968.9,1224L6968,1223.1L6952,1210.5L6936,1218.2L6928.8,1224L6920,1231.4L6910.7,1240L6904,1246.6L6895.1,1256L6888,1264.5L6882,1272L6872,1286.8L6871.2,1288L6861.5,1304L6856,1315.6L6854.9,1320L6852.1,1336L6851.7,1352L6851.6,1368L6851.7,1384L6851.8,1400L6851.7,1416L6851.7,1432L6851.4,1448L6850.9,1464L6849.9,1480L6850.2,1496L6853.7,1512L6856,1516.2L6872,1524.8L6877.4,1528L6888,1534.1L6904,1543.8L6904.3,1544L6920,1555.6L6925.3,1560L6936,1569.6L6942.2,1576L6952,1587.3L6955.5,1592L6963.9,1608L6968,1620.4L6969,1624L6969.5,1640L6968,1650.5L6966.9,1656L6958.9,1672L6952,1681.6L6946.2,1688L6936,1699L6930.5,1704L6920,1716.3L6916.6,1720L6906.3,1736L6904,1752L6910.8,1768L6920,1774L6936,1782.3L6939.5,1784L6952,1787.8L6968,1792.1L6984,1795.7L7000,1798.6L7009.7,1800L7016,1800.6L7032,1802L7048,1803L7064,1803.8L7080,1804.3L7096,1804.5L7112,1804.6L7128,1804.6L7144,1804.4L7160,1804.1L7176,1803.8L7192,1803.4L7208,1803.1L7224,1802.6L7240,1802.2L7256,1801.7L7272,1801.3L7288,1800.8L7304,1800.2L7310.5,1800Z","label":[7119.1,1825]},"L:3":{"path":"M5216.3,584L5224,583.1L5240,581.2L5256,579.2L5272,577.1L5288,574.8L5304,572.5L5320,570.1L5334,568L5336,567.6L5352,564.8L5368,562L5384,559.2L5400,556.3L5416,553.4L5424.9,552L5432,550.5L5448,547.4L5464,538.3L5465.5,536L5470.2,520L5473.9,504L5476.8,488L5479,472L5480,460.3L5480.5,456L5481.4,440L5481.4,424L5480.5,408L5480,403.4L5478.9,392L5476.6,376L5473.4,360L5468.9,344L5464,330.2L5463.3,328L5457.2,312L5449.3,296L5448,293.6L5440.7,280L5432,266.6L5430.3,264L5418.6,248L5416,244.8L5405.2,232L5400,226.5L5389.4,216L5384,210.9L5371.4,200L5368,197.2L5352,185.2L5350.2,184L5336,174.4L5324.8,168L5320,165.2L5304,156.9L5292.5,152L5288,150L5272,143.8L5256,139L5243.7,136L5240,134.9L5224,131.2L5208,128.5L5192,126.8L5176,125.9L5160,125.8L5144,126.6L5128,128.3L5112,130.9L5096,134.7L5091.5,136L5080,138.9L5064,144L5048,150.6L5045.2,152L5032,158.2L5016,167.7L5015.6,168L5000,178.1L4992.4,184L4984,190.6L4973.4,200L4968,205.1L4957.4,216L4952,222L4943.5,232L4936,242.2L4931.8,248L4921.6,264L4920,266.9L4912.5,280L4905.1,296L4904,298.7L4898.3,312L4892.7,328L4888.4,344L4888,345.7L4884.4,360L4881.3,376L4879.1,392L4877.8,408L4877.1,424L4877.1,440L4877.9,456L4879.2,472L4881.4,488L4884.2,504L4888,520L4888,520L4891.8,536L4896.6,552L4902.4,568L4904,571.8L4908.6,584L4920,594.3L4936,595L4952,595.5L4968,595.8L4984,595.9L5000,595.9L5016,595.8L5032,595.6L5048,595.2L5064,594.7L5080,594.1L5096,593.3L5112,592.5L5128,591.5L5144,590.4L5160,589.2L5176,587.9L5192,586.5L5208,584.9L5216.3,584Z","label":[5170.4,446.7]},"L:12":{"path":"M6505,2280L6518.3,2264L6520,2261.9L6530.5,2248L6536,2239.9L6541.3,2232L6551.4,2216L6552,2214.9L6560.6,2200L6568,2184.1L6568.1,2184L6575.4,2168L6581.5,2152L6584,2144.2L6586.9,2136L6591.8,2120L6595.8,2104L6599.1,2088L6600,2083.1L6602.4,2072L6605.3,2056L6607.6,2040L6609.4,2024L6610.7,2008L6611.7,1992L6612.3,1976L6612.6,1960L6612.5,1944L6612,1928L6611.2,1912L6610.1,1896L6608.5,1880L6606.6,1864L6604.2,1848L6601.3,1832L6600,1825.7L6598.4,1816L6584,1804.1L6578.8,1800L6568,1793.6L6553.3,1784L6552,1783.3L6536,1772.8L6529.5,1768L6520,1762.3L6504.8,1752L6504,1751.6L6488,1741.1L6480.9,1736L6472,1730.2L6457.6,1720L6456,1719L6440,1708.1L6434.3,1704L6424,1696.9L6411.5,1688L6408,1685.5L6392,1674.2L6388.9,1672L6376,1662.9L6366.2,1656L6360,1651.5L6344,1640.2L6343.7,1640L6328,1628.8L6320.8,1624L6312,1617.5L6298,1608L6296,1606.5L6280,1605.8L6276.6,1608L6264,1618.1L6256.5,1624L6248,1629.6L6232,1639.6L6231.2,1640L6216,1646.9L6200,1653L6189.7,1656L6184,1657.4L6168,1659.9L6152,1661.2L6136,1661.3L6120,1660.2L6104,1658.3L6090.8,1656L6088,1655.3L6072,1651L6056,1646.2L6040,1641.1L6024,1647L6017.7,1656L6008.1,1672L6008,1672.1L5999.1,1688L5992,1704L5992,1704L5985.1,1720L5979.6,1736L5976,1749.1L5975.1,1752L5970.9,1768L5967.8,1784L5965.6,1800L5964.1,1816L5963.3,1832L5963.1,1848L5963.5,1864L5964.4,1880L5965.9,1896L5968,1912L5970.5,1928L5973.7,1944L5976,1954.3L5977.1,1960L5980.5,1976L5984.4,1992L5988.8,2008L5992,2018.6L5993.3,2024L5997.9,2040L6003.6,2056L6008,2067.8L6012.2,2072L6024,2083.4L6027.6,2088L6040,2103.7L6040.2,2104L6047.7,2120L6056,2136L6056,2136L6060.8,2152L6067.2,2168L6071.2,2184L6072,2188.5L6073.6,2200L6076.7,2216L6083.9,2232L6088,2237.7L6102.3,2248L6104,2248.7L6120,2249L6136,2249.4L6152,2249.9L6168,2250.5L6184,2251.3L6200,2252.1L6216,2253.1L6232,2254.1L6248,2255.2L6264,2256.5L6280,2257.8L6296,2259.2L6312,2260.7L6328,2262.3L6343.6,2264L6344,2264L6360,2266L6376,2268.1L6392,2270.2L6408,2272.5L6424,2274.9L6440,2277.3L6456,2279.9L6456.9,2280L6472,2282.9L6488,2286.1L6504,2281.3L6505,2280ZM6500.7,2760L6504,2756.6L6512.6,2744L6520,2730.6L6521.5,2728L6529.1,2712L6535,2696L6536,2692.7L6540.7,2680L6545.2,2664L6548.5,2648L6550.7,2632L6551.9,2616L6552,2613.1L6552.4,2600L6552,2588.6L6551.9,2584L6550.5,2568L6548.3,2552L6544.9,2536L6540.3,2520L6536,2507.4L6535,2504L6529.3,2488L6522,2472L6520,2468L6504,2458.1L6488,2458L6472,2457.9L6456,2457.8L6440,2457.6L6424,2457.4L6408,2457.2L6392,2456.9L6376,2456.5L6360,2456L6359.5,2456L6344,2455.4L6328,2454.7L6312,2453.9L6296,2452.9L6280,2451.8L6264,2450.6L6248,2449.2L6232,2447.6L6216,2445.9L6200,2444L6184,2442L6169.4,2440L6168,2439.7L6152,2437L6136,2434.1L6120,2431.1L6104,2427.9L6088,2424.7L6084,2424L6072,2421.1L6056,2423.4L6055.6,2424L6044,2440L6040,2446.2L6033.6,2456L6025,2472L6024,2474.2L6017,2488L6010.7,2504L6008,2512.5L6005.3,2520L6000.8,2536L5997.5,2552L5995.3,2568L5994.6,2584L5997,2600L5998.9,2616L6000.9,2632L6003.2,2648L6005.5,2664L6007.7,2680L6008,2681.8L6012,2696L6018.7,2712L6024,2722.1L6037.1,2728L6040,2728.8L6056,2729.5L6072,2730.2L6088,2731.1L6104,2732L6120,2732.9L6136,2734L6152,2735.1L6168,2736.3L6184,2737.5L6200,2738.8L6216,2740.2L6232,2741.6L6248,2743L6258.6,2744L6264,2744.6L6280,2746.3L6296,2748L6312,2749.7L6328,2751.5L6344,2753.2L6360,2755L6376,2756.8L6392,2758.5L6405.7,2760L6408,2760.3L6424,2762.3L6440,2764.2L6456,2766.2L6472,2768.1L6488,2770L6500.7,2760Z","label":[6281.7,2146]},"L:6":{"path":"M6633.5,1800L6648,1794.4L6664,1787L6669.7,1784L6680,1778.2L6695.4,1768L6696,1767.7L6712,1757.5L6719.6,1752L6728,1745.6L6739.4,1736L6744,1732L6753.5,1720L6760,1712.3L6763.5,1704L6770.5,1688L6776,1675.7L6777.5,1672L6784.3,1656L6791.2,1640L6792,1638.2L6798,1624L6805,1608L6808,1601.1L6811.8,1592L6818.6,1576L6824,1563.1L6825.4,1560L6832.3,1544L6839,1528L6840,1525.5L6845.6,1512L6848.3,1496L6849.9,1480L6850.9,1464L6851.4,1448L6851.7,1432L6851.7,1416L6851.8,1400L6851.7,1384L6851.6,1368L6851.4,1352L6850.8,1336L6849.7,1320L6845.2,1304L6840,1291.3L6838.6,1288L6831.1,1272L6824,1259.4L6822.2,1256L6812.7,1240L6808,1233.1L6801.7,1224L6792,1211.7L6789.1,1208L6776,1193.2L6774.9,1192L6760,1177.3L6758.6,1176L6744,1162.8L6740.5,1160L6728,1150L6719.5,1144L6712,1138.6L6696,1128.8L6694.6,1128L6680,1119.9L6664,1112.6L6662.5,1112L6648,1105.7L6632,1099.9L6618.6,1096L6616,1095.1L6600,1090.2L6584,1086.3L6568,1083.3L6552,1081.1L6540,1080L6536,1079.5L6520,1078.4L6504,1078.2L6488,1078.7L6473.3,1080L6472,1080.1L6456,1081.8L6440,1084.3L6424,1087.6L6408,1092L6395.9,1096L6392,1097.2L6376,1103L6360,1110.3L6356.8,1112L6344,1118.7L6329.5,1128L6328,1129L6312,1140.3L6307.4,1144L6296,1153.5L6288.9,1160L6280,1168.7L6273,1176L6264,1185.6L6258.4,1192L6248,1205.6L6246.2,1208L6235.3,1224L6232,1229.4L6225.5,1240L6217.1,1256L6216,1258.3L6209.1,1272L6202.4,1288L6200,1294.7L6196.5,1304L6191.3,1320L6187,1336L6184,1349.1L6183.2,1352L6179.3,1368L6176.2,1384L6173.8,1400L6171.9,1416L6170.5,1432L6169.7,1448L6169.3,1464L6169.4,1480L6176.5,1496L6184,1501.9L6194.1,1512L6200,1516.4L6212.6,1528L6216,1530.7L6229.9,1544L6232,1545.7L6246.6,1560L6248,1561.2L6262.8,1576L6264,1577.1L6278.6,1592L6280,1593.2L6296,1606.5L6298,1608L6312,1617.5L6320.8,1624L6328,1628.8L6343.7,1640L6344,1640.2L6360,1651.5L6366.2,1656L6376,1662.9L6388.9,1672L6392,1674.2L6408,1685.5L6411.5,1688L6424,1696.9L6434.3,1704L6440,1708.1L6456,1719L6457.6,1720L6472,1730.2L6480.9,1736L6488,1741.1L6504,1751.6L6504.8,1752L6520,1762.3L6529.5,1768L6536,1772.8L6552,1783.3L6553.3,1784L6568,1793.6L6578.8,1800L6584,1804.1L6600,1812.4L6616,1807.2L6632,1800.7L6633.5,1800Z","label":[6514.9,1450.1]},"L:13":{"path":"M6189.7,1656L6200,1653L6216,1646.9L6231.2,1640L6232,1639.6L6248,1629.6L6256.5,1624L6264,1618.1L6276.6,1608L6277.2,1592L6264,1578.2L6262.6,1576L6248,1561.4L6246.6,1560L6232,1545.7L6229.9,1544L6216,1530.7L6212.6,1528L6200,1516.4L6194.1,1512L6184,1501.9L6175,1496L6168,1489.9L6154.6,1496L6152,1497.2L6136,1505.8L6126.6,1512L6120,1516.2L6104.8,1528L6104,1528.7L6088,1544L6088,1544L6073.9,1560L6072,1562.4L6061.9,1576L6056,1585.4L6051.9,1592L6043.3,1608L6040,1615.3L6035.9,1624L6038.9,1640L6040,1641.1L6056,1646.2L6072,1651L6088,1655.3L6090.8,1656L6104,1658.3L6120,1660.2L6136,1661.3L6152,1661.2L6168,1659.9L6184,1657.4L6189.7,1656ZM6073.9,2216L6073.6,2200L6072,2188.5L6071.2,2184L6067.2,2168L6060.8,2152L6056,2136L6056,2136L6047.7,2120L6040.2,2104L6040,2103.7L6027.6,2088L6024,2083.4L6012.2,2072L6008,2067.8L6005.9,2072L6006.8,2088L6008,2096.7L6009.6,2104L6012.6,2120L6017.6,2136L6024,2151.4L6024.3,2152L6032.5,2168L6040,2179.8L6043,2184L6055.8,2200L6056,2200.2L6070.4,2216L6072,2217.7L6073.9,2216Z","label":[6232.5,1937.3]},"L:8":{"path":"M4556.1,2376L4568,2372.6L4584,2368L4600,2363.4L4611.2,2360L4615.1,2344L4613.8,2328L4611.4,2312L4609.5,2296L4607.9,2280L4600.8,2264L4600,2262.2L4593.3,2248L4584.9,2232L4584,2230.8L4572.2,2216L4568,2211.6L4555.4,2200L4552,2196.8L4536.3,2184L4536,2183.8L4520,2173.4L4510.5,2168L4504,2164.2L4488,2156.4L4477.9,2152L4472,2149L4456,2142L4443.5,2136L4440,2133.6L4424,2121.8L4420.8,2120L4408,2106.6L4393.4,2104L4392,2103L4385.2,2088L4391.7,2072L4392,2071.8L4408,2065.7L4415.1,2056L4424,2050.7L4433.9,2040L4440,2036.3L4456,2026.7L4461.1,2024L4472,2020.4L4488,2014.9L4504,2009.5L4508.1,2008L4520,2004.9L4536,2000.5L4552,1996.1L4566.3,1992L4568,1991.6L4584,1987.6L4600,1983.4L4616,1978.9L4625.7,1976L4632,1974.4L4648,1970L4664,1965.2L4680,1960.2L4680.5,1960L4696,1955.3L4712,1950.3L4728,1944.9L4730.7,1944L4744,1939.7L4760,1934.5L4776,1929L4778.9,1928L4792,1923.7L4808,1918.3L4824,1912.9L4826.6,1912L4840,1907.5L4856,1902.2L4872,1896.7L4874.3,1896L4888,1891.4L4904,1885.9L4920,1880.3L4920.8,1880L4936,1874.6L4952,1867.7L4962,1864L4968,1861.4L4984,1855.4L5000,1850.3L5006.7,1848L5016,1843.9L5032,1834.8L5034.2,1832L5038,1816L5039.1,1800L5039.9,1784L5040.3,1768L5040.4,1752L5040,1736L5039.2,1720L5038,1704L5036,1688L5033.5,1672L5032,1664.2L5030.8,1656L5027.9,1640L5024.2,1624L5019.5,1608L5016,1598.1L5014,1592L5007.7,1576L5000,1560.3L4999.9,1560L4991.7,1544L4984,1531.5L4981.9,1528L4970.4,1512L4968,1508.8L4957.9,1496L4952,1489.2L4943.4,1480L4936,1472.6L4926.3,1464L4920,1458.7L4905.1,1448L4904,1447.2L4888,1436.5L4879.7,1432L4872,1427.6L4856,1420.1L4844.9,1416L4840,1414.2L4824,1409.3L4808,1405.6L4792,1403L4776,1401.2L4760,1400.2L4744,1400L4728,1400.5L4712,1401.7L4696,1403.7L4680,1406.5L4664,1410.2L4648,1415L4645.3,1416L4632,1420.2L4616,1426.4L4603.7,1432L4600,1433.6L4584,1441.6L4573.3,1448L4568,1450.8L4552,1460.5L4546.8,1464L4536,1470.7L4523,1480L4520,1482.2L4504,1494.9L4502.7,1496L4488,1508.3L4484,1512L4472,1523L4466.9,1528L4456,1539L4451.3,1544L4440,1556.7L4437.1,1560L4424.2,1576L4424,1576.3L4412.7,1592L4408,1599.2L4401.5,1608L4392,1623.2L4391.5,1624L4381.7,1640L4376,1651.1L4373.4,1656L4365.9,1672L4360,1687.2L4359.6,1688L4352.8,1704L4347.2,1720L4344,1730.8L4342.4,1736L4338,1752L4334.5,1768L4331.5,1784L4329.1,1800L4328,1808.9L4326.8,1816L4324.7,1832L4323.2,1848L4322,1864L4321.2,1880L4320.9,1896L4320.8,1912L4321.1,1928L4321.6,1944L4322.5,1960L4323.6,1976L4325.1,1992L4326.8,2008L4328,2017.5L4329.2,2024L4332.6,2040L4336,2056L4338.6,2072L4340.2,2088L4341.2,2104L4344,2116.6L4347.1,2120L4351.7,2136L4352.9,2152L4355.6,2168L4360,2182.5L4360.6,2184L4365.3,2200L4370.9,2216L4376,2228.3L4377.3,2232L4384.4,2248L4392,2263.1L4392.4,2264L4401,2280L4408,2290.7L4411.5,2296L4424,2311.9L4424.1,2312L4438,2328L4440,2330.1L4454.7,2344L4456,2345.2L4472,2357.9L4475,2360L4488,2368.3L4503,2376L4504,2376.5L4520,2380.4L4536,2378.6L4552,2376.6L4556.1,2376Z","label":[4675.3,1890.3]},"L:9":{"path":"M5688.7,2232L5704,2216.3L5704.2,2216L5713.3,2200L5720,2185.1L5720.5,2184L5727.5,2168L5733.6,2152L5736,2144.3L5738.9,2136L5743.6,2120L5747.6,2104L5751,2088L5752,2082.5L5754.2,2072L5757.9,2056L5760.6,2040L5763,2024L5765.4,2008L5767.5,1992L5768,1988.6L5770.3,1976L5774,1960L5777,1944L5780.1,1928L5783.2,1912L5784,1908.2L5786.7,1896L5790.3,1880L5793.9,1864L5797.5,1848L5800,1836.4L5801.5,1832L5806.7,1816L5811.6,1800L5816,1784.2L5816.1,1784L5821.3,1768L5825.8,1752L5829.6,1736L5832,1724.5L5833.2,1720L5836.7,1704L5839.5,1688L5841.8,1672L5843.4,1656L5844.4,1640L5844.7,1624L5844.4,1608L5843.4,1592L5841.6,1576L5838.8,1560L5835.1,1544L5832,1534.1L5830.6,1528L5825.9,1512L5820,1496L5816,1487.1L5812.9,1480L5804.4,1464L5800,1457.1L5794.6,1448L5784,1433.2L5783,1432L5769,1416L5768,1415L5752.5,1400L5752,1399.6L5736,1386.5L5732.6,1384L5720,1374.7L5709.3,1368L5704,1364.6L5688,1355.7L5680.2,1352L5672,1347.9L5656,1341.1L5641.1,1336L5640,1335.6L5624,1330.4L5608,1326.4L5592,1323.2L5576,1320.8L5568.5,1320L5560,1318.8L5544,1317.4L5528,1316.7L5512,1316.7L5506.2,1320L5496,1323.3L5480,1332.7L5475,1336L5464,1342L5448,1351.6L5447.3,1352L5432,1361.1L5420.9,1368L5416,1370.8L5400,1380.3L5394,1384L5384,1389.5L5368,1398.7L5365.7,1400L5352,1407.5L5336.5,1416L5336,1416.3L5320,1424.8L5306.2,1432L5304,1433.2L5288,1441.6L5275,1448L5272,1449.6L5256,1457.2L5241,1464L5240,1464.5L5224,1471.5L5208,1478.5L5203.7,1480L5192,1485.4L5176,1493.5L5171.8,1496L5161.4,1512L5160,1514.4L5152.6,1528L5145.4,1544L5144,1547.5L5137.7,1560L5131.1,1576L5128,1585.1L5125.4,1592L5120.4,1608L5116.5,1624L5113.6,1640L5112,1652.6L5111.5,1656L5109.8,1672L5108.8,1688L5108.6,1704L5109,1720L5110.1,1736L5111.8,1752L5112,1753.4L5113.7,1768L5116,1784L5118.7,1800L5121.9,1816L5125.6,1832L5128,1841.8L5129.4,1848L5133,1864L5137,1880L5141,1896L5144,1908.1L5144.8,1912L5147.9,1928L5150.8,1944L5153.6,1960L5156.3,1976L5159,1992L5160,1998.2L5161.3,2008L5163.8,2024L5166.1,2040L5169.2,2056L5172.5,2072L5176,2086.9L5176.2,2088L5179.7,2104L5184.2,2120L5189.3,2136L5192,2143.2L5195,2152L5201.5,2168L5208,2181.7L5209,2184L5217,2200L5224,2211.7L5226.5,2216L5236.8,2232L5240,2236.4L5256,2245.6L5272,2245.1L5288,2244.4L5304,2243.6L5320,2242.7L5336,2241.7L5352,2240.7L5368,2239.6L5384,2238.5L5400,2237.4L5416,2236.2L5432,2235.1L5448,2234L5464,2233L5480,2232L5480.2,2232L5496,2231.1L5512,2230.4L5528,2229.7L5544,2229.2L5560,2228.8L5576,2228.6L5592,2228.6L5608,2228.7L5624,2229.1L5640,2229.6L5656,2230.3L5672,2231.2L5684.1,2232L5688,2232.3L5688.7,2232Z","label":[5461.2,1777.2]},"L:17":{"path":"M6508.9,2456L6519,2440L6520,2432.6L6521.4,2424L6522.9,2408L6523.2,2392L6522.4,2376L6520.4,2360L6520,2357.7L6517.8,2344L6514,2328L6508.8,2312L6504,2300.3L6502,2296L6488,2286.1L6472,2282.9L6456.9,2280L6456,2279.9L6440,2277.3L6424,2274.9L6408,2272.5L6392,2270.2L6376,2268.1L6360,2266L6344,2264L6343.6,2264L6328,2262.3L6312,2260.7L6296,2259.2L6280,2257.8L6264,2256.5L6248,2255.2L6232,2254.1L6216,2253.1L6200,2252.1L6184,2251.3L6168,2250.5L6152,2249.9L6136,2249.4L6120,2249L6104,2248.7L6088,2262.2L6087,2264L6079,2280L6072.9,2296L6072,2298.8L6067.5,2312L6063.5,2328L6060.6,2344L6058.9,2360L6057.8,2376L6057.7,2392L6059,2408L6072,2421.1L6084,2424L6088,2424.7L6104,2427.9L6120,2431.1L6136,2434.1L6152,2437L6168,2439.7L6169.4,2440L6184,2442L6200,2444L6216,2445.9L6232,2447.6L6248,2449.2L6264,2450.6L6280,2451.8L6296,2452.9L6312,2453.9L6328,2454.7L6344,2455.4L6359.5,2456L6360,2456L6376,2456.5L6392,2456.9L6408,2457.2L6424,2457.4L6440,2457.6L6456,2457.8L6472,2457.9L6488,2458L6504,2458.1L6508.9,2456ZM6334,3528L6344,3526.1L6360,3522L6376,3516.5L6386.4,3512L6392,3509.6L6408,3501.3L6416.3,3496L6424,3491.3L6439,3480L6440,3479.2L6456,3465.3L6457.4,3464L6472,3448.8L6472.7,3448L6486.5,3432L6488,3429.9L6498,3416L6504,3405.8L6507.6,3400L6515.9,3384L6520,3374.5L6523,3368L6529.2,3352L6534.1,3336L6536,3328.1L6538.3,3320L6541.9,3304L6544.5,3288L6546.3,3272L6547.4,3256L6547.8,3240L6547.7,3224L6546.9,3208L6545.5,3192L6543.4,3176L6540.6,3160L6536.9,3144L6536,3140.3L6533.4,3128L6529,3112L6523.7,3096L6520,3086.3L6517.8,3080L6511.9,3064L6504.9,3048L6504,3046L6498.3,3032L6491.5,3016L6488,3007.3L6485.3,3000L6480.4,2984L6476.5,2968L6474.9,2952L6474.8,2936L6476.8,2920L6479.8,2904L6483.1,2888L6486.1,2872L6488,2862.2L6489.3,2856L6492.2,2840L6494.2,2824L6495,2808L6495.3,2792L6493.8,2776L6488,2770L6472,2768.1L6456,2766.2L6440,2764.2L6424,2762.3L6408,2760.3L6405.7,2760L6392,2758.5L6376,2756.8L6360,2755L6344,2753.2L6328,2751.5L6312,2749.7L6296,2748L6280,2746.3L6264,2744.6L6258.6,2744L6248,2743L6232,2741.6L6216,2740.2L6200,2738.8L6184,2737.5L6168,2736.3L6152,2735.1L6136,2734L6120,2732.9L6104,2732L6088,2731.1L6072,2730.2L6056,2729.5L6040,2728.8L6025.1,2744L6024,2756.8L6023.7,2760L6023.6,2776L6024,2782.8L6024.4,2792L6026.1,2808L6028.8,2824L6032.6,2840L6037.8,2856L6040,2861.7L6043.6,2872L6050.4,2888L6056,2899.5L6058.1,2904L6065.9,2920L6072,2931.9L6074,2936L6080.3,2952L6085.9,2968L6088,2978.4L6089,2984L6089.9,3000L6088.6,3016L6088,3019.4L6085.4,3032L6080.8,3048L6075.7,3064L6072,3076.8L6071,3080L6064.8,3096L6059.3,3112L6056,3122.8L6054.2,3128L6049.6,3144L6045,3160L6041.3,3176L6040,3182.5L6037.8,3192L6034.7,3208L6032.5,3224L6030.9,3240L6030,3256L6029.8,3272L6030.4,3288L6031.7,3304L6036,3320L6040,3335.3L6040.2,3336L6046.5,3352L6051.1,3368L6056,3381.9L6057,3384L6064.1,3400L6070.6,3416L6072,3419.5L6080.3,3432L6088,3441.5L6093.5,3448L6104,3459.5L6108.5,3464L6120,3474.6L6126.7,3480L6136,3487.3L6149.3,3496L6152,3497.8L6168,3507L6179.2,3512L6184,3514.2L6200,3520.4L6216,3524.9L6230.9,3528L6232,3528.3L6248,3531.3L6264,3533.2L6280,3533.9L6296,3533.5L6312,3532.1L6328,3529.4L6334,3528Z","label":[6274.2,2902.1]},"L:20":{"path":"M6971.7,3720L6984,3717.7L7000,3713.5L7016,3707.9L7025,3704L7032,3701L7048,3692.7L7055.4,3688L7064,3682.6L7078.1,3672L7080,3670.6L7096,3657.6L7097.7,3656L7112,3641.5L7113.4,3640L7126.8,3624L7128,3622.4L7138.6,3608L7144,3599.2L7148.5,3592L7157,3576L7160,3569.2L7164.5,3560L7171,3544L7176,3528L7176,3527.9L7180.9,3512L7184.6,3496L7187.1,3480L7176,3465.8L7174.9,3464L7163.7,3448L7160,3443.7L7152.8,3432L7144,3420.2L7141.5,3416L7130.1,3400L7128,3397.7L7118.3,3384L7112,3376.5L7106,3368L7096,3355.1L7093.9,3352L7081.4,3336L7080,3334.3L7069.1,3320L7064,3313.9L7056,3304L7048,3294.2L7043,3288L7032,3275L7029.4,3272L7016,3256.8L7015.3,3256L7000.8,3240L7000,3239L6986.3,3224L6984,3221.4L6971.1,3208L6968,3204.3L6956.2,3192L6952,3186.9L6941.7,3176L6936,3168.7L6928,3160L6920,3148.1L6916.7,3144L6908.4,3128L6904,3112.9L6903.7,3112L6900.9,3096L6902.7,3080L6904,3074.9L6906.1,3064L6910.2,3048L6915.6,3032L6920,3019.8L6921.1,3016L6925.8,3000L6930.6,2984L6935.4,2968L6936,2965.3L6938.5,2952L6941.3,2936L6943.4,2920L6944.7,2904L6945.9,2888L6946.2,2872L6946,2856L6945.9,2840L6945.5,2824L6945.9,2808L6946.5,2792L6948,2776L6950.4,2760L6952,2753.5L6954.1,2744L6958.7,2728L6964.3,2712L6968,2703.3L6970.8,2696L6977.5,2680L6984,2664.4L6984.2,2664L6990.7,2648L6997,2632L7000,2623.1L7002.3,2616L7006.7,2600L7010,2584L7012.4,2568L7013.9,2552L7014.1,2536L7013.3,2520L7011.9,2504L7009.6,2488L7006.5,2472L7002.9,2456L7000,2444.6L6998.7,2440L6994.1,2424L6985.4,2408L6984,2406.9L6968,2394.5L6964.9,2392L6952,2382.2L6943.7,2376L6936,2370.3L6922,2360L6920,2358.5L6904,2347.1L6899.4,2344L6888,2335.8L6876.4,2328L6872,2324.8L6856,2314.1L6852.5,2312L6840,2303.5L6828.2,2296L6824,2292.7L6808,2282.2L6804.1,2280L6792,2271.8L6779.6,2264L6776,2261.2L6760,2250.6L6754.5,2248L6744,2240.4L6730.9,2248L6728,2250L6712,2263.3L6711.2,2264L6696,2279.5L6695.5,2280L6682.5,2296L6680,2299.4L6670.9,2312L6664,2324.4L6661.9,2328L6654.1,2344L6648.1,2360L6648,2360.3L6642.5,2376L6638.3,2392L6635,2408L6632.6,2424L6632,2429.2L6630.6,2440L6629.2,2456L6628.3,2472L6628,2488L6628.1,2504L6628.7,2520L6629.5,2536L6630.7,2552L6632,2564.3L6632.3,2568L6634,2584L6636,2600L6638.5,2616L6641.6,2632L6645.3,2648L6648,2658L6649.4,2664L6653.7,2680L6658.6,2696L6664,2711.6L6664.1,2712L6669.2,2728L6674.4,2744L6680,2759.5L6680.2,2760L6683.8,2776L6686.7,2792L6688.9,2808L6690.7,2824L6691.3,2840L6691.7,2856L6691.8,2872L6692.1,2888L6693.2,2904L6694.4,2920L6696,2932.1L6696.4,2936L6699.1,2952L6702.6,2968L6708.2,2984L6712,2994.3L6714,3000L6720.4,3016L6727.2,3032L6728,3033.6L6735.1,3048L6743.1,3064L6744,3066.1L6750.2,3080L6755.5,3096L6755.8,3112L6752.4,3128L6744.7,3144L6744,3144.9L6732.7,3160L6728,3165.4L6719.2,3176L6712,3184.4L6705.7,3192L6696,3203.9L6692.8,3208L6680.9,3224L6680,3225.4L6670.1,3240L6664,3250.4L6660.6,3256L6652.3,3272L6648,3282.2L6645.3,3288L6639.4,3304L6634.7,3320L6632,3332.7L6631.2,3336L6628.1,3352L6626.2,3368L6625.2,3384L6625.1,3400L6625.9,3416L6627.4,3432L6629.9,3448L6632,3458L6633,3464L6636.5,3480L6641,3496L6646.6,3512L6648,3515.4L6652.5,3528L6659.4,3544L6664,3553.1L6667.2,3560L6675.9,3576L6680,3582.5L6685.7,3592L6696,3606.6L6697,3608L6709.3,3624L6712,3627.1L6723.5,3640L6728,3644.7L6739.9,3656L6744,3659.6L6760,3671.9L6760.2,3672L6776,3683.5L6783.4,3688L6792,3692.9L6808,3700.6L6816.8,3704L6824,3707.2L6840,3712.9L6856,3717.2L6870.5,3720L6872,3720.3L6888,3723.1L6904,3724.7L6920,3725.3L6936,3724.9L6952,3723.4L6968,3720.8L6971.7,3720Z","label":[6890.9,3043.6]},"L:7":{"path":"M4853.2,2376L4856,2374.7L4872,2366.6L4882.9,2360L4888,2357.1L4904,2346.7L4907.7,2344L4920,2335.8L4930.4,2328L4936,2324.2L4952,2312.2L4952.2,2312L4968,2297L4968.9,2296L4982.2,2280L4984,2277.7L4995.4,2264L5000,2257.7L5007.5,2248L5016,2235.7L5018.6,2232L5028.7,2216L5032,2210L5037.8,2200L5045.8,2184L5048,2179.1L5053.3,2168L5059.7,2152L5064,2138.9L5065,2136L5069.7,2120L5073.5,2104L5076.6,2088L5079,2072L5080,2063.6L5081.2,2056L5083.1,2040L5084.1,2024L5084.3,2008L5083.7,1992L5082.3,1976L5080.1,1960L5080,1959.7L5077.7,1944L5074.5,1928L5070.2,1912L5064.8,1896L5064,1894L5059.3,1880L5052.9,1864L5048,1853.8L5044.3,1848L5032,1834.8L5016,1843.9L5006.7,1848L5000,1850.3L4984,1855.4L4968,1861.4L4962,1864L4952,1867.7L4936,1874.6L4920.8,1880L4920,1880.3L4904,1885.9L4888,1891.4L4874.3,1896L4872,1896.7L4856,1902.2L4840,1907.5L4826.6,1912L4824,1912.9L4808,1918.3L4792,1923.7L4778.9,1928L4776,1929L4760,1934.5L4744,1939.7L4730.7,1944L4728,1944.9L4712,1950.3L4696,1955.3L4680.5,1960L4680,1960.2L4664,1965.2L4648,1970L4632,1974.4L4625.7,1976L4616,1978.9L4600,1983.4L4584,1987.6L4568,1991.6L4566.3,1992L4552,1996.1L4536,2000.5L4520,2004.9L4508.1,2008L4504,2009.5L4488,2014.9L4472,2020.4L4461.1,2024L4456,2026.7L4440,2036.3L4433.9,2040L4424,2050.7L4415.1,2056L4408,2065.7L4392,2071.8L4391.7,2072L4385.2,2088L4392,2103L4393.4,2104L4408,2106.6L4420.8,2120L4424,2121.8L4440,2133.6L4443.5,2136L4456,2142L4472,2149L4477.9,2152L4488,2156.4L4504,2164.2L4510.5,2168L4520,2173.4L4536,2183.8L4536.3,2184L4552,2196.8L4555.4,2200L4568,2211.6L4572.2,2216L4584,2230.8L4584.9,2232L4593.3,2248L4600,2262.2L4600.8,2264L4607.9,2280L4609.5,2296L4611.4,2312L4613.8,2328L4615.1,2344L4611.2,2360L4616,2361.4L4632,2364.7L4648,2366.7L4664,2368.2L4680,2369.4L4696,2370.4L4712,2371.3L4728,2372.1L4744,2373.1L4760,2374.3L4776,2375.8L4778.3,2376L4792,2377.5L4808,2379.4L4824,2381.6L4840,2380.8L4853.2,2376Z","label":[4695.6,2028.2]},"L:10":{"path":"M5353.8,2760L5368,2757.9L5384,2755.8L5400,2753.9L5416,2752.2L5432,2750.7L5448,2749.5L5464,2748.5L5480,2747.8L5496,2747.3L5512,2747L5528,2746.9L5544,2747L5560,2747.3L5576,2747.8L5592,2748.6L5608,2749.5L5624,2750.6L5640,2752L5656,2753.5L5672,2755.2L5688,2757.2L5704,2744.9L5704.5,2744L5712,2728L5716,2712L5718,2696L5720,2680L5720,2679.7L5722.3,2664L5725.2,2648L5728.6,2632L5732.5,2616L5736,2602.6L5736.8,2600L5741.9,2584L5747.2,2568L5752,2553.6L5752.7,2552L5757,2536L5758.7,2520L5759.2,2504L5759.1,2488L5758.5,2472L5757.3,2456L5755.5,2440L5753.1,2424L5752,2418.2L5750.5,2408L5747.7,2392L5744.3,2376L5740.2,2360L5736,2345.6L5735.6,2344L5731.1,2328L5725.9,2312L5720,2296.6L5719.8,2296L5714.3,2280L5708,2264L5704,2255.1L5701.1,2248L5688,2232.4L5684.1,2232L5672,2231.2L5656,2230.3L5640,2229.6L5624,2229.1L5608,2228.7L5592,2228.6L5576,2228.6L5560,2228.8L5544,2229.2L5528,2229.7L5512,2230.4L5496,2231.1L5480.2,2232L5480,2232L5464,2233L5448,2234L5432,2235.1L5416,2236.2L5400,2237.4L5384,2238.5L5368,2239.6L5352,2240.7L5336,2241.7L5320,2242.7L5304,2243.6L5288,2244.4L5272,2245.1L5256,2245.8L5249.8,2248L5240,2256L5234.4,2264L5224.6,2280L5224,2281L5215.1,2296L5208,2310.1L5207,2312L5199.2,2328L5193,2344L5192,2347L5187.2,2360L5182.5,2376L5178.8,2392L5176.1,2408L5176,2408.6L5173.6,2424L5171.9,2440L5171.1,2456L5171.1,2472L5171.9,2488L5173.4,2504L5175.7,2520L5176,2521.7L5178,2536L5180.9,2552L5184.4,2568L5188.6,2584L5192,2595.2L5193.4,2600L5198.3,2616L5203.9,2632L5208,2642.4L5210,2648L5216,2664L5223,2680L5224,2682.2L5229.8,2696L5237.5,2712L5240,2716.7L5245.6,2728L5254.6,2744L5256,2746.2L5264.4,2760L5272,2771.2L5288,2773.2L5304,2769.6L5320,2766.3L5336,2763.2L5352,2760.3L5353.8,2760Z","label":[5465.8,2475.9]},"L:16":{"path":"M5875.4,2808L5880,2807.6L5896,2804.5L5912,2799.5L5928,2792.2L5928.4,2792L5944,2782.8L5953.1,2776L5960,2770.3L5970.4,2760L5976,2753.6L5983.4,2744L5992,2730.1L5993.2,2728L6000.7,2712L6005.9,2696L6007.3,2680L6004.1,2664L6001.8,2648L5999.8,2632L5997.7,2616L5995.3,2600L5992.4,2584L5992,2582L5983.4,2568L5976,2558.5L5970.4,2552L5960,2541.8L5953,2536L5944,2529.2L5928.3,2520L5928,2519.8L5912,2512.6L5896,2507.6L5880,2504.5L5874.9,2504L5864,2503L5848,2503.2L5841.3,2504L5832,2505.1L5816,2508.6L5800,2514.2L5787.9,2520L5784,2521.9L5768,2532.1L5765.3,2536L5753.3,2552L5752,2553.6L5747.2,2568L5742,2584L5736.9,2600L5736,2602.6L5732.5,2616L5728.6,2632L5725.2,2648L5722.5,2664L5720,2679.7L5720,2680L5718.3,2696L5718,2712L5720,2722L5722.8,2728L5732.6,2744L5736,2748.5L5745.6,2760L5752,2766.5L5762.9,2776L5768,2779.9L5784,2790.1L5787.8,2792L5800,2797.9L5816,2803.4L5832,2807L5840.9,2808L5848,2808.9L5864,2809.1L5875.4,2808ZM5897.9,3640L5912,3637.3L5928,3632.8L5944,3626.4L5948.8,3624L5960,3618.5L5976,3608.3L5976.5,3608L5992,3596.2L5996.7,3592L6008,3580.9L6012.5,3576L6024,3561.7L6025.3,3560L6035.9,3544L6040,3536.3L6044.5,3528L6051.5,3512L6056,3498.2L6056.8,3496L6061.2,3480L6064.1,3464L6065.8,3448L6066.4,3432L6064.6,3416L6060.5,3400L6056.7,3384L6056,3381.9L6049.8,3368L6045,3352L6040.1,3336L6040,3335.6L6031.2,3320L6024,3304.3L6023.8,3304L6010.4,3288L6008,3285.4L5993.6,3272L5992,3270.6L5976,3258.6L5971.8,3256L5960,3248.9L5944,3241.4L5940.3,3240L5928,3235.3L5912,3230.9L5896,3228L5880,3226.6L5864,3226.5L5848,3227.7L5832,3230.3L5816,3234.4L5800.8,3240L5800,3240.3L5784,3247.3L5769.2,3256L5768,3256.7L5752,3267.9L5747.1,3272L5736,3282L5730,3288L5720,3299.5L5716.3,3304L5705.2,3320L5704,3322.1L5695.9,3336L5688.6,3352L5688,3353.7L5682.5,3368L5677.9,3384L5674.7,3400L5672.7,3416L5672,3428.9L5671.8,3432L5672,3443.8L5672.1,3448L5673.4,3464L5675.8,3480L5679.6,3496L5684.9,3512L5688,3519.2L5691.6,3528L5699.9,3544L5704,3550.5L5710.1,3560L5720,3572.7L5722.8,3576L5736,3589.8L5738.4,3592L5752,3603.6L5758.3,3608L5768,3614.6L5784,3623.3L5785.6,3624L5800,3630.5L5816,3635.7L5832,3639.3L5836.8,3640L5848,3641.7L5864,3642.8L5880,3642.3L5896,3640.4L5897.9,3640Z","label":[5857.3,3167.3]},"L:11":{"path":"M4728.9,2872L4744,2860.6L4749.4,2856L4760,2847.8L4769.1,2840L4776,2834.8L4789.3,2824L4792,2821.9L4808,2809.5L4809.9,2808L4824,2797.3L4831.2,2792L4840,2785.3L4852.7,2776L4856,2773.5L4872,2761.9L4875,2760L4888,2746.3L4890.3,2744L4899.4,2728L4904,2718L4907,2712L4913.8,2696L4919,2680L4920,2676.2L4923.7,2664L4927.4,2648L4930,2632L4931.6,2616L4932.3,2600L4932.2,2584L4931.2,2568L4929.3,2552L4926.4,2536L4922.4,2520L4920,2512.7L4917.5,2504L4911.8,2488L4904.3,2472L4904,2471.4L4896.3,2456L4888,2442.8L4886.3,2440L4875,2424L4872,2420.2L4861.8,2408L4856,2401.8L4846.1,2392L4840,2388.2L4824,2382.3L4808,2379.4L4792,2377.5L4778.3,2376L4776,2375.8L4760,2374.3L4744,2373.1L4728,2372.1L4712,2371.3L4696,2370.7L4680,2370.2L4664,2369.9L4648,2369.7L4632,2369.7L4616,2369.7L4600,2370.7L4584,2372.6L4568,2374.6L4556.1,2376L4552,2376.6L4536,2378.7L4520,2382L4504,2389.2L4500.6,2392L4488,2403.4L4483.3,2408L4472,2420.1L4468.5,2424L4456,2439.7L4455.8,2440L4444.2,2456L4440,2463L4434.3,2472L4425.9,2488L4424,2492.3L4418.3,2504L4412,2520L4408,2533.1L4407,2536L4402.3,2552L4398.8,2568L4396.4,2584L4394.8,2600L4394.1,2616L4394.2,2632L4395.1,2648L4396.9,2664L4399.7,2680L4403.5,2696L4408,2709.8L4408.6,2712L4414.2,2728L4421.4,2744L4424,2748.8L4429.6,2760L4439.8,2776L4440,2776.2L4451.2,2792L4456,2797.8L4464.9,2808L4472,2815.4L4481.2,2824L4488,2830L4501.2,2840L4504,2842.1L4520,2852.6L4526.4,2856L4536,2861.2L4552,2868.1L4563.7,2872L4568,2873.7L4584,2878.7L4600,2882.2L4616,2884.6L4632,2885.9L4648,2886.3L4664,2885.7L4680,2884.2L4696,2881.7L4712,2878L4728,2872.9L4728.9,2872Z","label":[4654,2600]},"L:15":{"path":"M4962.9,3512L4968,3510.8L4984,3505.4L5000,3497.9L5003.4,3496L5016,3488.8L5028.3,3480L5032,3477.2L5046.8,3464L5048,3462.8L5061.4,3448L5064,3444.6L5073.2,3432L5080,3420.4L5082.6,3416L5090.3,3400L5096,3384.3L5096.1,3384L5100.9,3368L5104.3,3352L5106.3,3336L5107.1,3320L5106.7,3304L5105.3,3288L5102.6,3272L5098.6,3256L5096,3247.6L5093.8,3240L5087.8,3224L5080.1,3208L5080,3207.9L5071.5,3192L5064,3180.1L5061.3,3176L5050,3160L5048,3157.3L5037.8,3144L5032,3136.4L5025.1,3128L5016,3115.8L5012.9,3112L5002.7,3096L5000,3089.6L4995.8,3080L4993.4,3064L4995,3048L4999.6,3032L5000,3031.1L5005.9,3016L5012.5,3000L5016,2989.6L5017.8,2984L5023.8,2968L5028.2,2952L5031.3,2936L5032,2928.9L5033,2920L5032.6,2904L5032,2896.4L5031.4,2888L5028.6,2872L5023.9,2856L5017.2,2840L5016,2837.8L5008.2,2824L5000,2812.6L4996.4,2808L4984,2794.9L4980.8,2792L4968,2781.7L4959.2,2776L4952,2771.7L4936,2764.1L4923.9,2760L4920,2758.7L4904,2755L4888,2754.2L4877.9,2760L4872,2762.2L4856,2773.5L4852.7,2776L4840,2785.3L4831.2,2792L4824,2797.3L4809.9,2808L4808,2809.5L4792,2821.9L4789.3,2824L4776,2834.8L4769.1,2840L4760,2847.8L4749.4,2856L4744,2861.9L4729.3,2872L4728,2877.2L4725,2888L4723.8,2904L4723.7,2920L4725.6,2936L4728,2947.4L4728.9,2952L4733.7,2968L4740,2984L4744,2993.1L4747.1,3000L4755.3,3016L4760,3024.9L4763.9,3032L4771.8,3048L4776,3059.9L4777.5,3064L4779.8,3080L4778,3096L4776,3101.8L4772.6,3112L4764.8,3128L4760,3136.1L4755.7,3144L4746.4,3160L4744,3164.2L4737.4,3176L4729.5,3192L4728,3195.4L4722.4,3208L4716.5,3224L4712.1,3240L4712,3240.3L4708.8,3256L4706.2,3272L4704.8,3288L4704.6,3304L4705.5,3320L4707.7,3336L4711.2,3352L4712,3354.6L4715.6,3368L4721.4,3384L4728,3398.1L4728.9,3400L4737.5,3416L4744,3425.8L4748.2,3432L4760,3446.6L4761.2,3448L4776,3463.2L4776.9,3464L4792,3476.8L4796.4,3480L4808,3488.1L4822.3,3496L4824,3497L4840,3504.5L4856,3510L4863.8,3512L4872,3514.3L4888,3517.2L4904,3518.7L4920,3518.8L4936,3517.6L4952,3514.9L4962.9,3512Z","label":[4888.7,3166.3]},"L:14":{"path":"M5581.3,3256L5592,3250.7L5608,3240.3L5608.4,3240L5624,3228.5L5629.1,3224L5640,3211.6L5642.9,3208L5653.6,3192L5656,3188.1L5663.2,3176L5670,3160L5672,3154.5L5675.9,3144L5680.4,3128L5683.8,3112L5686.6,3096L5688,3086.8L5689.1,3080L5691.6,3064L5694,3048L5696.5,3032L5699.2,3016L5702,3000L5704,2988.8L5705,2984L5708.3,2968L5711.3,2952L5714,2936L5716.3,2920L5718,2904L5719.1,2888L5719.5,2872L5719.2,2856L5718.2,2840L5716.3,2824L5713.4,2808L5709.4,2792L5704,2776L5704,2776L5693.2,2760L5688,2757.2L5672,2755.2L5656,2753.5L5640,2752L5624,2750.6L5608,2749.5L5592,2748.6L5576,2747.8L5560,2747.3L5544,2747L5528,2746.9L5512,2747L5496,2747.3L5480,2747.8L5464,2748.5L5448,2749.5L5432,2750.7L5416,2752.2L5400,2753.9L5384,2755.8L5368,2757.9L5353.8,2760L5352,2760.3L5336,2763.2L5320,2766.3L5304,2769.6L5288,2773.2L5280.6,2776L5272,2791.3L5271.8,2792L5269.1,2808L5267.5,2824L5267,2840L5267.4,2856L5268.8,2872L5271.2,2888L5272,2892.1L5274.1,2904L5277.7,2920L5282.2,2936L5287.6,2952L5288,2953L5293,2968L5299.1,2984L5304,2996L5305.5,3000L5311.6,3016L5318,3032L5320,3037.3L5323.8,3048L5329.3,3064L5334.7,3080L5336,3083.8L5339.7,3096L5344.7,3112L5350.2,3128L5352,3132.9L5355.9,3144L5363.6,3160L5368,3169.4L5371.1,3176L5381.4,3192L5384,3195.9L5392.5,3208L5400,3217L5406.6,3224L5416,3231.7L5428.3,3240L5432,3242.8L5448,3252.6L5455.3,3256L5464,3259.9L5480,3265.2L5496,3268.4L5512,3269.9L5528,3269.8L5544,3267.9L5560,3264.2L5576,3258.5L5581.3,3256Z","label":[5491,2910.6]},"2:I":{"path":"M2644.8,5560L2648,5559.1L2664,5554L2680,5547.8L2688.3,5544L2696,5541L2712,5533.9L2723.2,5528L2728,5525.5L2744,5516.2L2750.3,5512L2760,5506.1L2774.2,5496L2776,5494.7L2792,5481.5L2793.6,5480L2808,5466.5L2810.5,5464L2824,5450.3L2826.2,5448L2839.8,5432L2840,5431.8L2851,5416L2856,5407.8L2862,5400L2872,5385.8L2873.2,5384L2883.3,5368L2888,5359.1L2892,5352L2900,5336L2904,5326.5L2907.2,5320L2914,5304L2919.5,5288L2920,5286.4L2924.9,5272L2929.3,5256L2932.8,5240L2935.4,5224L2936,5219.3L2937.6,5208L2939.2,5192L2940.1,5176L2940.5,5160L2940.4,5144L2939.7,5128L2938.6,5112L2937,5096L2936,5088L2935.1,5080L2933,5064L2930.5,5048L2927.6,5032L2924.1,5016L2920.2,5000L2920,4999.4L2916.1,4984L2911.2,4968L2905.6,4952L2904,4948L2900.4,4936L2894.8,4920L2888.1,4904L2888,4903.7L2881.8,4888L2874.4,4872L2872,4867.4L2866.8,4856L2858.1,4840L2856,4836.5L2848.3,4824L2840,4812.4L2837.1,4808L2825.7,4792L2824,4789.9L2813.2,4776L2808,4769.8L2799.7,4760L2792,4751.5L2785,4744L2776,4735.3L2768,4728L2760,4720.5L2750.1,4712L2744,4706.8L2729.8,4696L2728,4694.6L2712,4683.6L2705.9,4680L2696,4673.7L2680,4665.1L2677.6,4664L2664,4656.7L2648,4649.8L2643,4648L2632,4643.4L2616,4638L2600,4633.9L2590.6,4632L2584,4630.5L2568,4627.7L2552,4625.9L2536,4625L2520,4625L2504,4626L2488,4627.8L2472,4630.7L2466.7,4632L2456,4634.3L2440,4638.7L2424,4644.4L2415.8,4648L2408,4651L2392,4658.4L2381.9,4664L2376,4667.3L2360,4677.7L2356.8,4680L2344,4689.3L2336,4696L2328,4702.8L2318.3,4712L2312,4718L2302.1,4728L2296,4734.9L2288.3,4744L2280,4755.2L2276.5,4760L2266,4776L2264,4779.3L2256.1,4792L2248,4807.9L2248,4808L2239.7,4824L2232.9,4840L2232,4842.3L2226.3,4856L2220.6,4872L2216,4887.5L2215.8,4888L2210.6,4904L2206.2,4920L2202.6,4936L2200,4949.9L2199.6,4952L2196.6,4968L2194.2,4984L2192.4,5000L2191,5016L2190.1,5032L2189.7,5048L2189.6,5064L2189.9,5080L2190.7,5096L2191.8,5112L2193.4,5128L2195.4,5144L2197.8,5160L2200,5172.3L2200.5,5176L2203.2,5192L2206.2,5208L2209.6,5224L2213.5,5240L2216,5249.1L2217.5,5256L2221.6,5272L2226.1,5288L2231.3,5304L2232,5306L2236.2,5320L2241.9,5336L2248,5350.2L2248.7,5352L2255,5368L2262.9,5384L2264,5385.9L2270.9,5400L2279.6,5416L2280,5416.8L2288.7,5432L2296,5442.5L2299.7,5448L2311.8,5464L2312,5464.2L2325,5480L2328,5483.2L2340.8,5496L2344,5499.1L2359,5512L2360,5512.8L2376,5524.3L2382.2,5528L2392,5534.8L2408,5543.8L2408.5,5544L2424,5552.2L2440,5558.6L2444.1,5560L2456,5563.6L2472,5567.4L2488,5570.3L2504,5572.2L2520,5573.5L2536,5574L2552,5574L2568,5573.3L2584,5572L2600,5570.1L2616,5567.3L2632,5563.7L2644.8,5560Z","label":[2547.4,5109.8]},"2:III":{"path":"M4165.7,5848L4168,5847.8L4184,5845.6L4200,5842.6L4216,5838.5L4232,5833.3L4235.4,5832L4248,5827.5L4257,5816L4264,5806.3L4267.6,5800L4275.3,5784L4280,5774.9L4283,5768L4289.9,5752L4296,5738.2L4296.8,5736L4302.9,5720L4308.5,5704L4312,5694L4313.8,5688L4318.8,5672L4323.2,5656L4327.2,5640L4328,5636.5L4330.8,5624L4334.1,5608L4337.1,5592L4339.7,5576L4342.2,5560L4344,5547.1L4344.4,5544L4346.7,5528L4348.8,5512L4350.9,5496L4352.9,5480L4355,5464L4357.3,5448L4359.5,5432L4360,5428.8L4362.2,5416L4365.1,5400L4368.4,5384L4371.9,5368L4375.8,5352L4376,5351.1L4380.7,5336L4386.3,5320L4392,5304.9L4392.4,5304L4400.1,5288L4408,5272.4L4408.3,5272L4418.4,5256L4424,5246.9L4429.6,5240L4440,5226.3L4442.3,5224L4455.7,5208L4456,5207.1L4462.9,5192L4465.5,5176L4468.1,5160L4470.5,5144L4472,5132.7L4472.7,5128L4474.7,5112L4476.3,5096L4477.3,5080L4477.8,5064L4477.7,5048L4477,5032L4475.6,5016L4473.6,5000L4472,4991.2L4470.8,4984L4467.3,4968L4462.8,4952L4456.8,4936L4456,4934L4451,4920L4443.8,4904L4440,4897L4435.4,4888L4425.3,4872L4424,4870.1L4414.2,4856L4408,4848.3L4401.1,4840L4392,4830.3L4385.8,4824L4376,4814.8L4368.1,4808L4360,4801.3L4347.1,4792L4344,4789.8L4328,4779.9L4320.5,4776L4312,4771.3L4296,4763.9L4285.1,4760L4280,4757.8L4264,4752.1L4248,4747.8L4232,4744.6L4228.2,4744L4216,4741.8L4200,4740L4184,4739.1L4168,4739.1L4152,4740.1L4136,4742L4124.9,4744L4120,4744.7L4104,4748L4088,4752.3L4072,4758L4067.3,4760L4056,4763.8L4040,4770.4L4029,4776L4024,4778.5L4008,4788L4002.1,4792L3992,4798.9L3980.6,4808L3976,4811.6L3962,4824L3960,4825.9L3946,4840L3944,4842.2L3932,4856L3928,4861.2L3919.7,4872L3912,4883.8L3909.1,4888L3899.4,4904L3896,4910.7L3890.9,4920L3883.6,4936L3880,4945.4L3877.4,4952L3871.8,4968L3866.9,4984L3864,4996.9L3863,5000L3858.6,5016L3854.6,5032L3851.5,5048L3848.7,5064L3848,5068.1L3845.6,5080L3842.6,5096L3839.5,5112L3836.3,5128L3833.1,5144L3832,5149.2L3829.4,5160L3825.4,5176L3821.3,5192L3817.4,5208L3816,5213.6L3812.6,5224L3807.8,5240L3803.4,5256L3800,5270.9L3799.7,5272L3796,5288L3793,5304L3790.5,5320L3788.7,5336L3787.4,5352L3786.7,5368L3786.5,5384L3786.7,5400L3787.4,5416L3788.6,5432L3790.2,5448L3792.3,5464L3794.9,5480L3798,5496L3800,5505.1L3801.2,5512L3804.3,5528L3807.8,5544L3811.9,5560L3816,5573.7L3816.6,5576L3821,5592L3826.2,5608L3832,5622.8L3832.4,5624L3838.3,5640L3845.6,5656L3848,5660.6L3853.3,5672L3862.7,5688L3864,5690.1L3871.5,5704L3880,5716.9L3882,5720L3894,5736L3896,5738.6L3906.8,5752L3912,5757.6L3922.2,5768L3928,5773.7L3939.7,5784L3944,5787.7L3960,5799.9L3960.1,5800L3976,5810.7L3985.7,5816L3992,5819.5L4008,5827.2L4020.9,5832L4024,5833.3L4040,5838.8L4056,5843L4072,5846.1L4086.6,5848L4088,5848.2L4104,5850L4120,5850.8L4136,5850.7L4152,5849.7L4165.7,5848Z","label":[4138.1,5305.3]},"2:II":{"path":"M3406,5608L3416,5607.6L3432,5606.1L3448,5603.9L3464,5600.9L3480,5596.9L3495.3,5592L3496,5591.8L3512,5586.1L3528,5578.8L3533.3,5576L3544,5570.9L3560,5561.4L3562.2,5560L3576,5551.8L3587.1,5544L3592,5540.3L3606.3,5528L3608,5526.5L3623,5512L3624,5511L3637.8,5496L3640,5493.3L3650.8,5480L3656,5472.8L3662.6,5464L3672,5448.7L3672.4,5448L3681.9,5432L3688,5419.1L3689.6,5416L3697,5400L3702.8,5384L3704,5380.2L3708.2,5368L3712.6,5352L3716.1,5336L3718.6,5320L3720,5308.2L3720.6,5304L3722.3,5288L3723.3,5272L3723.6,5256L3723.2,5240L3722.1,5224L3720.3,5208L3720,5206.1L3718.5,5192L3716.2,5176L3713.4,5160L3710,5144L3705.8,5128L3704,5121.9L3701,5112L3695.2,5096L3688.1,5080L3688,5079.8L3681.1,5064L3672.6,5048L3672,5047L3663.9,5032L3656,5019.8L3654,5016L3644.3,5000L3640,4993.9L3632.6,4984L3624,4973.6L3619.3,4968L3608,4956L3604,4952L3592,4940.1L3587.5,4936L3576,4926L3568.3,4920L3560,4913.4L3546.3,4904L3544,4902.4L3528,4892.6L3518.9,4888L3512,4884.3L3496,4876.9L3482.7,4872L3480,4870.8L3464,4864.9L3448,4860.3L3432,4856.7L3428.1,4856L3416,4853.3L3400,4850.6L3384,4848.9L3368,4847.9L3352,4847.6L3336,4848.1L3320,4849.3L3304,4851.3L3288,4854.2L3280.3,4856L3272,4857.6L3256,4861.4L3240,4866.2L3224.7,4872L3224,4872.2L3208,4878.3L3192,4885.9L3188.1,4888L3176,4894.4L3161.1,4904L3160,4904.7L3144,4915.9L3138.9,4920L3128,4928.7L3119.9,4936L3112,4943.5L3103.7,4952L3096,4960.6L3089.7,4968L3080,4980.9L3077.7,4984L3066.9,5000L3064,5005.1L3057.5,5016L3049.6,5032L3048,5035.9L3042.4,5048L3036.5,5064L3032,5079.3L3031.8,5080L3027.8,5096L3024.8,5112L3022.7,5128L3021.2,5144L3020.5,5160L3020.3,5176L3020.9,5192L3022,5208L3023.8,5224L3026.4,5240L3029.7,5256L3032,5264.8L3033.7,5272L3038.2,5288L3043.8,5304L3048,5314.4L3049.9,5320L3055.9,5336L3063.2,5352L3064,5353L3075,5368L3080,5371L3096,5381.9L3098.5,5384L3112,5393.3L3120.7,5400L3128,5404.8L3142.8,5416L3144,5416.8L3160,5429L3163.6,5432L3176,5441.5L3183.9,5448L3192,5454.4L3203.5,5464L3208,5467.7L3222.6,5480L3224,5481.2L3240,5494.5L3241.8,5496L3256,5508.8L3259.8,5512L3272,5523.3L3277.5,5528L3288,5537.9L3295.1,5544L3304,5552.3L3313.4,5560L3320,5566.3L3331.8,5576L3336,5580.4L3349.3,5592L3352,5594.9L3368,5607.6L3377.7,5608L3384,5608.4L3400,5608.4L3406,5608Z","label":[3370.1,5223.6]},"2:IV":{"path":"M3138.1,6360L3144,6359.2L3160,6356L3176,6351.5L3192,6345.4L3195,6344L3208,6338.3L3224,6329.2L3225.8,6328L3240,6319.2L3249.5,6312L3256,6306.9L3268.3,6296L3272,6292.5L3284,6280L3288,6275.6L3298,6264L3304,6255.7L3309.6,6248L3319.3,6232L3320,6230.8L3328.3,6216L3335.4,6200L3336,6198.4L3342.1,6184L3347.5,6168L3351.7,6152L3352,6150.3L3355.5,6136L3358.5,6120L3360.6,6104L3361.9,6088L3362.7,6072L3362.9,6056L3362.5,6040L3361.7,6024L3360.5,6008L3359.2,5992L3357.5,5976L3355.5,5960L3353.5,5944L3352,5929.1L3351.9,5928L3350.7,5912L3349.9,5896L3349.6,5880L3349.8,5864L3350.6,5848L3351.9,5832L3352,5831.4L3354,5816L3356.6,5800L3359.2,5784L3361.9,5768L3364.2,5752L3366.4,5736L3368,5721.6L3368.2,5720L3370,5704L3371.1,5688L3371.6,5672L3371.4,5656L3370.5,5640L3368.8,5624L3368,5619.3L3366.5,5608L3352,5595.2L3349.3,5592L3336,5580.4L3331.8,5576L3320,5566.3L3313.4,5560L3304,5552.3L3295.1,5544L3288,5537.9L3277.5,5528L3272,5523.3L3259.8,5512L3256,5508.8L3241.8,5496L3240,5494.5L3224,5481.2L3222.6,5480L3208,5467.7L3203.5,5464L3192,5454.4L3183.9,5448L3176,5441.5L3163.6,5432L3160,5429L3144,5416.8L3142.8,5416L3128,5404.8L3120.7,5400L3112,5393.3L3098.5,5384L3096,5381.9L3080,5371L3071.9,5368L3064,5362.9L3048,5364.4L3032,5367.2L3028.7,5368L3016,5370.6L3000,5375.1L2984,5380.9L2977.1,5384L2968,5387.7L2952,5395.7L2944.9,5400L2936,5405.1L2920.4,5416L2920,5416.3L2904,5428.7L2900.2,5432L2888,5443L2882.9,5448L2872,5459.9L2868.5,5464L2856.1,5480L2856,5480.1L2844.9,5496L2840,5504.4L2835.4,5512L2827.3,5528L2824,5535.6L2820.1,5544L2814,5560L2809.2,5576L2808,5581.1L2804.9,5592L2801.5,5608L2798.9,5624L2797.2,5640L2796.2,5656L2795.8,5672L2796,5688L2796.6,5704L2797.8,5720L2799.3,5736L2801.1,5752L2802.9,5768L2804.8,5784L2806.5,5800L2807.9,5816L2808,5818.8L2808.5,5832L2808.7,5848L2808.5,5864L2808,5875.3L2807.8,5880L2806.5,5896L2805.1,5912L2803.7,5928L2802.4,5944L2801.3,5960L2800.5,5976L2800.1,5992L2800.2,6008L2800.7,6024L2801.7,6040L2803.3,6056L2805.4,6072L2808,6086.3L2808.3,6088L2811.3,6104L2815.1,6120L2819.9,6136L2824,6147.1L2825.5,6152L2831.4,6168L2839,6184L2840,6186.1L2846.5,6200L2855.8,6216L2856,6216.3L2865.4,6232L2872,6241.2L2876.8,6248L2888,6261.9L2889.7,6264L2904,6279.2L2904.8,6280L2920,6294.7L2921.5,6296L2936,6308.2L2941.1,6312L2952,6319.5L2966.9,6328L2968,6328.7L2984,6337.8L2998.3,6344L3000,6344.8L3016,6350.9L3032,6355.5L3048,6358.8L3056.3,6360L3064,6361.5L3080,6363.3L3096,6363.9L3112,6363.5L3128,6361.8L3138.1,6360Z","label":[3074.8,5866.2]},"2:V":{"path":"M5050.3,6152L5064,6149.8L5080,6145.9L5096,6140.5L5106.1,6136L5112,6133.6L5128,6125.8L5137.4,6120L5144,6115.7L5158.9,6104L5160,6103.1L5176,6088.3L5176.3,6088L5192,6072.2L5192.2,6072L5205.1,6056L5208,6051.8L5216.3,6040L5224,6027L5225.8,6024L5234.6,6008L5240,5996.4L5242.2,5992L5249.3,5976L5255.5,5960L5256,5958.6L5261.7,5944L5266.8,5928L5271,5912L5272,5908.1L5275.5,5896L5279.4,5880L5282.7,5864L5285.4,5848L5287.7,5832L5288,5829.7L5290,5816L5292,5800L5293.4,5784L5294.5,5768L5295.2,5752L5295.6,5736L5295.7,5720L5295.5,5704L5294.9,5688L5294.5,5672L5293.7,5656L5292.6,5640L5291.4,5624L5290.3,5608L5289.6,5592L5289,5576L5289.3,5560L5290.2,5544L5291.9,5528L5294.5,5512L5297.7,5496L5301.6,5480L5304,5470.3L5305.7,5464L5310,5448L5314.2,5432L5318,5416L5320,5406.6L5321.9,5400L5326.1,5384L5329.4,5368L5332.1,5352L5334.2,5336L5335.8,5320L5336,5316.7L5337,5304L5337.8,5288L5338.1,5272L5337.9,5256L5337.3,5240L5336.3,5224L5336,5221.3L5334.9,5208L5333.2,5192L5331.1,5176L5328.3,5160L5324.9,5144L5320.7,5128L5320,5125.7L5316.7,5112L5312,5096L5306.2,5080L5304,5074.7L5299.8,5064L5292.3,5048L5288,5040.2L5283.8,5032L5274.1,5016L5272,5012.9L5263.6,5000L5256,4990L5251.4,4984L5240,4971.1L5237.1,4968L5224,4954.3L5221.6,4952L5208,4939.4L5203.8,4936L5192,4926.8L5181.7,4920L5176,4916L5160,4906.3L5155.6,4904L5144,4897.8L5128,4890.9L5119.8,4888L5112,4884.8L5096,4879.7L5080,4875.8L5064,4873.1L5053.9,4872L5048,4871.2L5032,4870.2L5016,4870.1L5000,4871L4991.6,4872L4984,4872.8L4968,4875.2L4952,4878.7L4936,4883.3L4923.1,4888L4920,4889L4904,4895.3L4888,4903.4L4886.9,4904L4872,4911.6L4858.7,4920L4856,4921.5L4840,4931.7L4834,4936L4824,4943.7L4814.4,4952L4808,4957.4L4796.7,4968L4792,4972.5L4780.6,4984L4776,4988.6L4765.1,5000L4760,5005.9L4751.3,5016L4744,5025.3L4738.6,5032L4728,5046.8L4727.1,5048L4716.2,5064L4712,5071L4706.2,5080L4697.2,5096L4696,5098.2L4688,5112L4680.5,5128L4680,5129.1L4673,5144L4666.8,5160L4664,5168.9L4661.3,5176L4656.1,5192L4652,5208L4649,5224L4648,5230.5L4646.5,5240L4648,5246.3L4649.5,5256L4655.8,5272L4662.6,5288L4664,5291.1L4668.9,5304L4675.1,5320L4680,5332.3L4681.2,5336L4686.8,5352L4692.3,5368L4696,5379.6L4697.3,5384L4701.8,5400L4705.8,5416L4709.3,5432L4712,5446.8L4712.2,5448L4714.4,5464L4716,5480L4717,5496L4717.3,5512L4716.9,5528L4716.1,5544L4714.8,5560L4713.1,5576L4712,5585.3L4711.2,5592L4708.9,5608L4706.5,5624L4704.1,5640L4701.5,5656L4699.1,5672L4696.7,5688L4696,5693.7L4694.4,5704L4692.3,5720L4691.1,5736L4693.1,5752L4696,5761.9L4697.8,5768L4703.1,5784L4709.3,5800L4712,5806.3L4715.8,5816L4722.8,5832L4728,5842.8L4730.2,5848L4737.4,5864L4744,5878.1L4744.8,5880L4751.2,5896L4759.1,5912L4760,5914.1L4765.4,5928L4772.2,5944L4776,5952.2L4779.2,5960L4786.8,5976L4792,5986.7L4794.4,5992L4803,6008L4808,6016L4812.8,6024L4822.4,6040L4824,6042.4L4833,6056L4840,6065.1L4845.5,6072L4856,6083.1L4861.1,6088L4872,6098.5L4878.4,6104L4888,6111.9L4899.8,6120L4904,6122.8L4920,6131.7L4930,6136L4936,6138.7L4952,6144.6L4968,6148.8L4984,6151.7L4986.5,6152L5000,6153.9L5016,6154.8L5032,6154.3L5048,6152.5L5050.3,6152Z","label":[4986.7,5448.9]},"2:VI":{"path":"M4525.2,6728L4536,6725.2L4552,6719.6L4568,6712L4568.1,6712L4584,6703.7L4595.6,6696L4600,6693.4L4616,6682.2L4618.7,6680L4632,6668L4636,6664L4648,6651.1L4650.7,6648L4663.8,6632L4664,6631.7L4674.8,6616L4680,6607L4684.2,6600L4692.3,6584L4696,6576.2L4700.2,6568L4706.8,6552L4712,6536L4712,6536L4717.7,6520L4722.3,6504L4726.1,6488L4728,6479.2L4729.8,6472L4733.5,6456L4736.8,6440L4739.7,6424L4742.3,6408L4744,6396.4L4744.7,6392L4747.4,6376L4749.7,6360L4751.7,6344L4753.4,6328L4754.9,6312L4756.1,6296L4757,6280L4757.6,6264L4757.8,6248L4757.8,6232L4757.3,6216L4756.5,6200L4755.2,6184L4753.5,6168L4751.3,6152L4748.5,6136L4745,6120L4744,6116.2L4741.3,6104L4737.1,6088L4731.9,6072L4728,6061.9L4725.9,6056L4719.6,6040L4712,6024.4L4711.8,6024L4704.2,6008L4696,5993.1L4695.4,5992L4686.6,5976L4680,5965.1L4677,5960L4667.1,5944L4664,5939.1L4657.3,5928L4648,5912L4648,5912L4641.8,5896L4637.1,5880L4635.8,5864L4637.3,5848L4641.8,5832L4647,5816L4648,5814.3L4656.4,5800L4664,5786.3L4665.3,5784L4675.4,5768L4680,5760L4683.9,5752L4688.7,5736L4691.9,5720L4694.4,5704L4696,5693.7L4696.7,5688L4699.1,5672L4701.5,5656L4704.1,5640L4706.5,5624L4708.9,5608L4711.2,5592L4712,5585.3L4713.1,5576L4714.8,5560L4716.1,5544L4716.9,5528L4717.3,5512L4717,5496L4716,5480L4714.4,5464L4712.2,5448L4712,5446.8L4709.3,5432L4705.8,5416L4701.8,5400L4697.3,5384L4696,5379.6L4692.3,5368L4686.8,5352L4681.2,5336L4680,5332.3L4675.1,5320L4668.9,5304L4664,5291.1L4662.6,5288L4655.8,5272L4649.3,5256L4648,5252.3L4634.4,5240L4632,5238.2L4616,5229.4L4603.4,5224L4600,5222.3L4584,5215.7L4568,5210.7L4556.5,5208L4552,5206.7L4536,5203.4L4520,5201.2L4504,5200.1L4488,5199.9L4472,5200.6L4456,5207.6L4455.7,5208L4442.3,5224L4440,5226.3L4429.6,5240L4424,5246.9L4418.4,5256L4408.3,5272L4408,5272.4L4400.1,5288L4392.4,5304L4392,5304.9L4386.3,5320L4380.7,5336L4376,5351.1L4375.8,5352L4371.9,5368L4368.4,5384L4365.1,5400L4362.2,5416L4360,5428.8L4359.5,5432L4357.3,5448L4355,5464L4352.9,5480L4350.9,5496L4348.8,5512L4346.7,5528L4344.4,5544L4344,5547.1L4342.2,5560L4339.7,5576L4337.1,5592L4334.1,5608L4330.8,5624L4328,5636.5L4327.2,5640L4323.2,5656L4318.8,5672L4313.8,5688L4312,5694L4308.5,5704L4302.9,5720L4296.8,5736L4296,5738.2L4289.9,5752L4283,5768L4280,5774.9L4275.3,5784L4267.6,5800L4264,5806.3L4257,5816L4251.2,5832L4253.8,5848L4254.6,5864L4253,5880L4248.9,5896L4248,5898.4L4242.5,5912L4234.7,5928L4232,5932.9L4225.7,5944L4216.8,5960L4216,5961.5L4207.6,5976L4200,5990.8L4199.3,5992L4191.3,6008L4184.5,6024L4184,6025.2L4177.7,6040L4172.1,6056L4168,6070.6L4167.5,6072L4163.1,6088L4159.7,6104L4157,6120L4155,6136L4153.5,6152L4152.6,6168L4152.1,6184L4152,6200L4152.3,6216L4152.8,6232L4153.7,6248L4154.9,6264L4156.3,6280L4158,6296L4160.1,6312L4162.4,6328L4165.1,6344L4168,6359L4168.2,6360L4170.9,6376L4174.1,6392L4177.6,6408L4181.6,6424L4184,6433L4185.6,6440L4189.8,6456L4194.3,6472L4199.4,6488L4200,6489.7L4204.2,6504L4210.1,6520L4216,6534.3L4216.6,6536L4222.8,6552L4230.7,6568L4232,6570.5L4238.6,6584L4247.8,6600L4248,6600.3L4257.4,6616L4264,6625.2L4268.8,6632L4280,6645.5L4282.2,6648L4296,6662.4L4297.7,6664L4312,6677.3L4315.2,6680L4328,6689.1L4339.7,6696L4344,6699L4360,6708.5L4367.3,6712L4376,6716.4L4392,6722.8L4408,6727.6L4409.9,6728L4424,6731.6L4440,6734.3L4456,6735.7L4472,6736L4488,6735.1L4504,6733L4520,6729.6L4525.2,6728Z","label":[4457,5997.3]},"3:I":{"path":"M3132.1,7960L3144,7957.5L3160,7952.9L3176,7946.7L3181.7,7944L3192,7940.1L3208,7930.7L3211.2,7928L3224,7917.5L3230.4,7912L3240,7904.3L3250.2,7896L3256,7891.3L3270,7880L3272,7878.1L3288,7865.5L3289.9,7864L3304,7850.7L3308,7848L3320,7833.3L3321.2,7832L3333.3,7816L3336,7812L3344.3,7800L3352,7787.4L3354.2,7784L3364.2,7768L3368,7761.2L3373.6,7752L3382.1,7736L3384,7732.2L3389.6,7720L3396,7704L3400,7693.2L3402.5,7688L3409.5,7672L3415.4,7656L3416,7654.2L3421.7,7640L3427,7624L3431.3,7608L3432,7605L3435.5,7592L3439.1,7576L3442.1,7560L3444.4,7544L3446.1,7528L3447.3,7512L3448,7496.7L3448,7496L3448.3,7480L3448,7465.4L3448,7464L3447.2,7448L3446,7432L3444.3,7416L3442,7400L3439.2,7384L3435.8,7368L3432,7353.3L3431.7,7352L3427.9,7336L3423.2,7320L3417.5,7304L3416,7300.1L3411.6,7288L3404.6,7272L3400,7262.7L3397.2,7256L3389.6,7240L3384,7229.9L3380.8,7224L3371.1,7208L3368,7203.4L3360.5,7192L3352,7180.5L3348.7,7176L3336,7160.4L3335.7,7160L3321.4,7144L3320,7142.6L3304.2,7128L3304,7127.8L3288,7113.9L3285.6,7112L3272,7101.3L3264.3,7096L3256,7090.5L3240,7081.5L3236.9,7080L3224,7073.3L3208,7066.6L3200.4,7064L3192,7060.6L3176,7055.5L3160,7051.6L3144,7048.8L3137.6,7048L3128,7046.5L3112,7045.2L3096,7044.8L3080,7045.3L3064,7046.9L3057.4,7048L3048,7049.2L3032,7052L3016,7055.9L3000,7060.9L2991.9,7064L2984,7066.8L2968,7073.7L2956.2,7080L2952,7082L2936,7091L2928.3,7096L2920,7101.5L2906.4,7112L2904,7113.7L2888,7126.5L2886.2,7128L2872,7141L2869,7144L2856,7158.1L2854.3,7160L2841.1,7176L2840,7177.4L2828.7,7192L2824,7199L2817.8,7208L2808.4,7224L2808,7224.8L2799.2,7240L2792,7255.2L2791.6,7256L2783.9,7272L2777.8,7288L2776,7293.4L2772,7304L2766.9,7320L2762.6,7336L2760,7347.8L2758.9,7352L2755.2,7368L2752.1,7384L2749.6,7400L2747.6,7416L2746,7432L2744.8,7448L2744,7462.2L2743.9,7464L2743.2,7480L2743,7496L2743.1,7512L2743.6,7528L2744,7535.3L2744.4,7544L2745.4,7560L2746.8,7576L2748.5,7592L2750.6,7608L2753.1,7624L2756.1,7640L2759.7,7656L2760,7657L2762.8,7672L2766.4,7688L2770.8,7704L2775.9,7720L2776,7720.2L2781.1,7736L2787.4,7752L2792,7761.4L2794.9,7768L2802.5,7784L2808,7793.8L2811.2,7800L2820.9,7816L2824,7820.4L2832,7832L2840,7842.5L2844.2,7848L2856,7860.9L2859,7864L2872,7877.3L2874.8,7880L2888,7892.2L2892.6,7896L2904,7905.3L2913.4,7912L2920,7916.4L2936,7925.6L2940.9,7928L2952,7934.2L2968,7941.5L2974.6,7944L2984,7948.1L3000,7953.7L3016,7957.9L3026.5,7960L3032,7961.2L3048,7963.6L3064,7965L3080,7965.4L3096,7964.9L3112,7963.5L3128,7960.9L3132.1,7960Z","label":[3084,7502.4]},"3:II":{"path":"M4412.9,8280L4424,8279.3L4440,8277.2L4456,8274.1L4472,8269.7L4487.5,8264L4488,8263.8L4504,8256.9L4519.7,8248L4520,8247.9L4536,8237.8L4541.4,8232L4552,8216.9L4552.3,8216L4559.4,8200L4565.2,8184L4568,8175.3L4570.1,8168L4575.5,8152L4580.4,8136L4584,8125L4585.5,8120L4591.2,8104L4597.6,8088L4600,8081.7L4603.8,8072L4610.8,8056L4616,8044.2L4618,8040L4626.5,8024L4632,8014.1L4635.8,8008L4645.6,7992L4648,7988.1L4656.5,7976L4664,7965.4L4668.5,7960L4680,7946.1L4682.1,7944L4696,7928.9L4697,7928L4712,7912.7L4712.7,7912L4722.7,7896L4728,7881.6L4728.8,7880L4736.6,7864L4743.5,7848L4744,7846.8L4750.3,7832L4756.6,7816L4760,7805.7L4762.5,7800L4769,7784L4774.6,7768L4776,7763.5L4780,7752L4785,7736L4789.2,7720L4792,7707.5L4792.9,7704L4796.3,7688L4799.2,7672L4801.6,7656L4803.5,7640L4805.1,7624L4806.3,7608L4807.1,7592L4807.6,7576L4807.7,7560L4807.3,7544L4806.6,7528L4805.3,7512L4803.4,7496L4800.8,7480L4797.3,7464L4792.9,7448L4792,7445.2L4788.5,7432L4783.3,7416L4776.7,7400L4776,7398.4L4770.3,7384L4762.5,7368L4760,7363.6L4754.3,7352L4744.8,7336L4744,7334.7L4734.1,7320L4728,7312.1L4722,7304L4712,7292L4708.4,7288L4696,7274.8L4693.3,7272L4680,7259.5L4675.9,7256L4664,7245.7L4656.7,7240L4648,7233.1L4634.9,7224L4632,7222L4616,7212L4608.4,7208L4600,7203.2L4584,7195.3L4576,7192L4568,7188.1L4552,7181.4L4536,7176.1L4535.6,7176L4520,7171.2L4504,7167.2L4488,7164.2L4472,7161.9L4456,7160.3L4450.3,7160L4440,7159.3L4424,7159.1L4408,7159.6L4403.7,7160L4392,7160.9L4376,7162.9L4360,7165.8L4344,7169.8L4328,7175.1L4325.7,7176L4312,7180.9L4296,7188.1L4288.8,7192L4280,7195.8L4264,7204L4257.3,7208L4248,7214.1L4235,7224L4232,7226.3L4216.4,7240L4216,7240.3L4200,7255.1L4199.1,7256L4184.7,7272L4184,7272.8L4171.8,7288L4168,7292.9L4159.6,7304L4152,7316.2L4149.4,7320L4139.7,7336L4136,7342.7L4130.5,7352L4122.4,7368L4120,7373.3L4114.7,7384L4107.9,7400L4104,7410.7L4101.8,7416L4095.5,7432L4090.4,7448L4088,7456L4085.1,7464L4080,7480L4075.7,7496L4072,7511.6L4071.9,7512L4067.7,7528L4064,7544L4060.9,7560L4058.2,7576L4056,7591L4055.8,7592L4053.2,7608L4051.1,7624L4049.3,7640L4048,7656L4047,7672L4046.3,7688L4046,7704L4046,7720L4046.5,7736L4047.3,7752L4048.5,7768L4050.1,7784L4052.2,7800L4054.8,7816L4056,7822.3L4057.6,7832L4060.6,7848L4064.3,7864L4068.7,7880L4072,7890.7L4073.3,7896L4077.8,7912L4088,7922.1L4094.7,7928L4104,7933.9L4117.1,7944L4120,7946L4136,7958.9L4137.1,7960L4152,7972.9L4155,7976L4168,7988.1L4171.6,7992L4184,8005.2L4186.3,8008L4199.8,8024L4200,8024.2L4211.8,8040L4216,8046L4222.4,8056L4232,8071.4L4232.4,8072L4240.8,8088L4248,8102.5L4248.7,8104L4256.3,8120L4262.6,8136L4264,8140.2L4268.3,8152L4274.2,8168L4278.9,8184L4280,8188L4283.9,8200L4288.2,8216L4291.6,8232L4294.8,8248L4296,8252.1L4308.2,8264L4312,8265.6L4328,8271L4344,8275L4360,8277.9L4376,8279.6L4383.4,8280L4392,8280.6L4408,8280.4L4412.9,8280Z","label":[4415.5,7663.4]},"3:V":{"path":"M4743.4,9336L4744,9335.8L4760,9327.4L4772.7,9320L4776,9318.4L4792,9309.4L4800.7,9304L4808,9299.7L4824,9289.3L4825.9,9288L4840,9278.5L4849.1,9272L4856,9267.4L4872,9256.2L4872.2,9256L4888,9244L4893.4,9240L4904,9231.5L4913.9,9224L4920,9218.9L4933.8,9208L4936,9206.2L4952,9193.8L4954.7,9192L4968,9180.9L4974.8,9176L4984,9168.5L4995.6,9160L5000,9146.8L5001.1,9144L5005,9128L5008.5,9112L5011.8,9096L5014.9,9080L5016,9074L5018.2,9064L5021.7,9048L5024.9,9032L5027.8,9016L5030.4,9000L5032,8988.6L5032.8,8984L5035.3,8968L5037.4,8952L5038.9,8936L5039.8,8920L5040.2,8904L5040.1,8888L5039.3,8872L5038.1,8856L5036.2,8840L5033.7,8824L5032,8815L5031,8808L5028.5,8792L5025.7,8776L5022.6,8760L5019.2,8744L5016,8728.2L5016,8728L5013.7,8712L5011.7,8696L5010.2,8680L5008.7,8664L5000,8650.3L4998.6,8648L4988.2,8632L4984,8625.9L4978.8,8616L4970,8600L4968,8596.7L4961.9,8584L4955,8568L4952,8561.4L4948.6,8552L4942.4,8536L4936.3,8520L4936,8519.3L4930.1,8504L4923.7,8488L4920,8479.4L4917.1,8472L4910.4,8456L4904,8444.8L4901.4,8440L4892.8,8424L4888,8415.9L4883.4,8408L4872.8,8392L4872,8390.8L4861.8,8376L4856,8367.2L4851.1,8360L4841,8344L4840,8342.3L4831.7,8328L4824.1,8312L4824,8311.6L4818,8296L4813.9,8280L4811.7,8264L4810.6,8248L4810.9,8232L4811.7,8216L4812.8,8200L4813.8,8184L4815.3,8168L4816.8,8152L4817.9,8136L4818.9,8120L4819.6,8104L4820,8088L4820.3,8072L4820.4,8056L4820.2,8040L4819.8,8024L4819.2,8008L4818.4,7992L4817.4,7976L4816.2,7960L4814.9,7944L4813.4,7928L4809.7,7912L4808,7910L4792,7906.4L4776,7904.1L4760,7903L4744,7903.1L4728,7904.4L4714,7912L4712,7912.7L4697,7928L4696,7928.9L4682.1,7944L4680,7946.1L4668.5,7960L4664,7965.4L4656.5,7976L4648,7988.1L4645.6,7992L4635.8,8008L4632,8014.1L4626.5,8024L4618,8040L4616,8044.2L4610.8,8056L4603.8,8072L4600,8081.7L4597.6,8088L4591.2,8104L4585.5,8120L4584,8125L4580.4,8136L4575.5,8152L4570.1,8168L4568,8175.3L4565.2,8184L4559.4,8200L4552.4,8216L4552,8217.8L4548,8232L4548.7,8248L4548.7,8264L4546.5,8280L4540.6,8296L4536,8305.3L4532.6,8312L4522.6,8328L4520,8331.6L4511.4,8344L4504,8354.5L4500.2,8360L4489.4,8376L4488,8378.2L4479.1,8392L4472,8404.1L4469.7,8408L4461.1,8424L4456,8435.4L4453.8,8440L4447.3,8456L4441.9,8472L4440,8478L4436.3,8488L4431.6,8504L4427.8,8520L4424.7,8536L4424,8540.5L4421.9,8552L4419.5,8568L4417.5,8584L4415.8,8600L4414.4,8616L4413,8632L4411.6,8648L4410.3,8664L4408.9,8680L4408,8690.2L4407.3,8696L4405.4,8712L4403.6,8728L4402.1,8744L4400.9,8760L4400,8776L4399.5,8792L4399.5,8808L4399.9,8824L4401,8840L4402.6,8856L4404.8,8872L4407.8,8888L4408,8889.1L4410.9,8904L4414.6,8920L4418.8,8936L4423.9,8952L4424,8952.2L4428.1,8968L4432.6,8984L4437.7,9000L4440,9007.2L4442.3,9016L4446.6,9032L4451.2,9048L4456,9063.4L4456.2,9064L4461.2,9080L4467,9096L4472,9108L4473.5,9112L4480.3,9128L4488,9142.8L4488.6,9144L4498.6,9160L4504,9168.7L4508.4,9176L4518.6,9192L4520,9193.9L4530,9208L4536,9215.7L4542.4,9224L4552,9235.3L4556,9240L4568,9252.9L4570.9,9256L4584,9268.2L4588.4,9272L4600,9282.8L4606,9288L4616,9296.4L4625.9,9304L4632,9308.5L4648,9319L4649.8,9320L4664,9328.8L4678.2,9336L4680,9336.9L4696,9344.3L4712,9349.9L4728,9344.1L4743.4,9336Z","label":[4718.7,8728.5]},"3:IX":{"path":"M3821.4,8504L3832,8502L3848,8497.8L3864,8492.2L3873.3,8488L3880,8485.4L3896,8477.6L3905.5,8472L3912,8468L3928,8456.3L3928.3,8456L3944,8443L3947.3,8440L3960,8427.5L3963.3,8424L3976,8409.1L3976.9,8408L3989,8392L3992,8387.5L3999.6,8376L4008,8360.7L4008.4,8360L4016.7,8344L4023.2,8328L4024,8325.6L4029.3,8312L4034.1,8296L4036,8280L4032,8264L4027.1,8248L4024,8238L4022.4,8232L4018.1,8216L4013.7,8200L4009.4,8184L4008,8179L4005.3,8168L4001.4,8152L3997.4,8136L3993.6,8120L3992,8113.3L3989.9,8104L3986.3,8088L3982.7,8072L3979.2,8056L3976,8041.3L3975.7,8040L3971.7,8024L3964.5,8008L3960,8002.6L3948.9,7992L3944,7987.7L3929.2,7976L3928,7975.1L3912,7964.2L3904.4,7960L3896,7955L3880,7947.1L3872.2,7944L3864,7940.4L3848,7934.8L3832,7930.7L3817.4,7928L3816,7927.7L3800,7925.3L3784,7924L3768,7923.9L3752,7924.8L3736,7926.9L3730.8,7928L3720,7929.8L3704,7933.7L3688,7939L3676.3,7944L3672,7945.7L3656,7953.3L3644.8,7960L3640,7962.7L3624,7973.3L3620.4,7976L3608,7986.1L3601.5,7992L3592,8002L3589.7,8008L3584.9,8024L3580.3,8040L3576,8055L3575.7,8056L3571.3,8072L3567,8088L3562.8,8104L3560,8115.2L3558.8,8120L3554.9,8136L3551.2,8152L3547.6,8168L3544.3,8184L3544,8185.8L3541.1,8200L3538,8216L3535.3,8232L3532.9,8248L3531,8264L3529.7,8280L3529.9,8296L3534.4,8312L3540.1,8328L3544,8337.2L3546.6,8344L3553.8,8360L3560,8371.4L3562.4,8376L3571.9,8392L3576,8398.1L3582.8,8408L3592,8419.7L3595.5,8424L3608,8437.7L3610.3,8440L3624,8452.9L3627.8,8456L3640,8465.8L3649.3,8472L3656,8476.3L3672,8484.8L3679.5,8488L3688,8491.9L3704,8497.6L3720,8501.9L3731.1,8504L3736,8505.2L3752,8507.7L3768,8508.9L3784,8508.9L3800,8507.7L3816,8505.2L3821.4,8504ZM3754.6,9912L3768,9898.1L3769.5,9896L3783.9,9880L3784,9880L3797.4,9864L3800,9861.4L3810.6,9848L3816,9842L3823.4,9832L3832,9821.6L3836,9816L3848,9800.3L3848.2,9800L3859.8,9784L3864,9778.3L3871.1,9768L3880,9755.4L3882.3,9752L3893.2,9736L3896,9731.8L3904,9720L3912,9707.5L3914.4,9704L3924.7,9688L3928,9682.5L3935.1,9672L3944,9657.5L3945.1,9656L3955.3,9640L3960,9631.6L3965.3,9624L3975.4,9608L3976,9606.8L3986.1,9592L3992,9581.2L3995.9,9576L4003.2,9560L3996.8,9544L3992,9534.1L3989.2,9528L3980.6,9512L3976,9504.7L3970.6,9496L3960,9481.6L3958.7,9480L3945.1,9464L3944,9462.9L3928.8,9448L3928,9447.3L3912,9434.1L3909,9432L3896,9423L3883.3,9416L3880,9414.1L3864,9406.5L3848,9400.8L3845.1,9400L3832,9396.1L3816,9392.7L3800,9390.8L3784,9390.1L3768,9390.6L3752,9392.4L3736,9395.5L3720.8,9400L3720,9400.2L3704,9405.7L3688,9413.1L3682.9,9416L3672,9422L3657.6,9432L3656,9433.1L3640,9446.2L3638.1,9448L3624,9462.1L3622.2,9464L3609,9480L3608,9481.4L3597.7,9496L3592,9505.7L3588.2,9512L3580.1,9528L3576,9538L3573.4,9544L3567.5,9560L3562.9,9576L3560,9589.2L3559.3,9592L3556.1,9608L3554,9624L3552.7,9640L3552.2,9656L3552.5,9672L3553.7,9688L3555.7,9704L3558.7,9720L3560,9725.2L3562.3,9736L3566.8,9752L3572.6,9768L3576,9775.8L3579.4,9784L3587.4,9800L3592,9807.7L3596.9,9816L3608,9831.5L3608.3,9832L3621.5,9848L3624,9850.7L3637.4,9864L3640,9866.4L3656,9879.3L3657,9880L3672,9890.4L3682.1,9896L3688,9899.4L3704,9906.8L3718.7,9912L3720,9912.5L3736,9917.1L3752,9915.3L3754.6,9912Z","label":[3774.8,8783.8]},"3:VI":{"path":"M3454.6,9240L3464,9236.9L3480,9229.8L3490.1,9224L3496,9220.6L3512,9209.3L3513.6,9208L3528,9195.3L3531.3,9192L3544,9177.6L3545.3,9176L3556.7,9160L3560,9155L3567,9144L3574.5,9128L3576,9123.9L3580.8,9112L3585.7,9096L3589.2,9080L3591.7,9064L3592,9060.8L3593.5,9048L3595,9032L3595.4,9016L3595.3,9000L3594.7,8984L3593.9,8968L3593,8952L3592.2,8936L3592,8931.3L3591.7,8920L3591.5,8904L3591.6,8888L3592,8872.8L3592,8872L3592.8,8856L3593.7,8840L3594.8,8824L3595.6,8808L3596.2,8792L3596.3,8776L3595.9,8760L3594.9,8744L3593.2,8728L3592,8720.6L3590.7,8712L3588.1,8696L3584.6,8680L3580.4,8664L3576,8650.3L3575.3,8648L3569.9,8632L3564.2,8616L3560,8605.3L3558.1,8600L3552.1,8584L3545.8,8568L3544,8563.4L3539.9,8552L3534.9,8536L3529.6,8520L3528,8514.8L3524.9,8504L3520.4,8488L3516.1,8472L3512,8456.9L3511.8,8456L3508.3,8440L3505.4,8424L3503.1,8408L3501.5,8392L3502.4,8376L3504,8360L3507.3,8344L3511.5,8328L3512,8326.7L3518.4,8312L3526,8296L3528,8290.1L3529.3,8280L3530.9,8264L3532.9,8248L3535.3,8232L3538,8216L3541.1,8200L3544,8185.8L3544.3,8184L3547.6,8168L3551.2,8152L3554.9,8136L3558.8,8120L3560,8115.2L3562.8,8104L3567,8088L3571.3,8072L3575.7,8056L3576,8055L3580.3,8040L3584.9,8024L3588.8,8008L3588.5,7992L3582.8,7976L3576,7961.2L3575.5,7960L3567.1,7944L3560,7933L3556.7,7928L3544.2,7912L3544,7911.8L3529.1,7896L3528,7894.9L3512,7881.1L3510.5,7880L3496,7869.6L3486.3,7864L3480,7860.4L3464,7852.8L3450.7,7848L3448,7847L3432,7842.5L3416,7839.5L3400,7837.8L3384,7837.3L3368,7837.8L3352,7839.6L3336,7842.5L3320,7846.9L3318.1,7848L3304,7854.9L3291.2,7864L3288,7866L3272,7878.4L3270,7880L3256,7891.3L3250.2,7896L3240,7904.3L3230.4,7912L3224,7918.7L3212.1,7928L3208,7933L3196.4,7944L3192,7951.2L3186.6,7960L3178.4,7976L3176,7981.4L3171.1,7992L3164.9,8008L3160,8023.5L3159.8,8024L3155.1,8040L3151.3,8056L3148.4,8072L3146.2,8088L3144.7,8104L3144,8118.1L3143.9,8120L3143,8136L3143.3,8152L3144,8163.5L3144.2,8168L3145.6,8184L3147.7,8200L3150.3,8216L3153.6,8232L3157.3,8248L3160,8258.7L3161.2,8264L3165,8280L3168.6,8296L3171.8,8312L3174.1,8328L3175.1,8344L3175.2,8360L3174.3,8376L3172.9,8392L3170.7,8408L3168.4,8424L3166.4,8440L3164.8,8456L3163.7,8472L3163.2,8488L3163.3,8504L3164,8520L3165.2,8536L3167.5,8552L3169.2,8568L3171,8584L3172.7,8600L3174.3,8616L3175.5,8632L3175.9,8648L3176,8652.1L3176.2,8664L3176.3,8680L3176.1,8696L3176,8707.6L3175.9,8712L3175.5,8728L3175.3,8744L3175.2,8760L3175.3,8776L3175.5,8792L3175.7,8808L3176,8824L3176,8824.6L3176.7,8840L3176.5,8856L3176.2,8872L3176,8878.7L3175.7,8888L3174.9,8904L3174,8920L3173.1,8936L3172.2,8952L3171.6,8968L3171.3,8984L3171.4,9000L3172.2,9016L3173.7,9032L3176,9045.3L3176.4,9048L3179.2,9064L3183,9080L3188.1,9096L3192,9105.9L3194.3,9112L3201.7,9128L3208,9139.1L3210.8,9144L3222.3,9160L3224,9162.3L3234.8,9176L3240,9181.7L3250.1,9192L3256,9197.4L3269.1,9208L3272,9210.2L3288,9220.9L3293.7,9224L3304,9229.7L3320,9236.6L3330.3,9240L3336,9242L3352,9246.2L3368,9248.9L3384,9250.3L3400,9250.3L3416,9249.1L3432,9246.5L3448,9242.4L3454.6,9240Z","label":[3365.3,8538.7]},"3:VII":{"path":"M4206.6,8312L4216,8309.5L4232,8303.6L4247.4,8296L4248,8295.7L4264,8286.3L4272.8,8280L4280,8274.5L4291.8,8264L4294.8,8248L4291.6,8232L4288.2,8216L4283.9,8200L4280,8188L4278.9,8184L4274.2,8168L4268.3,8152L4264,8140.2L4262.6,8136L4256.3,8120L4248.7,8104L4248,8102.5L4240.8,8088L4232.4,8072L4232,8071.4L4222.4,8056L4216,8046L4211.8,8040L4200,8024.2L4199.8,8024L4186.3,8008L4184,8005.2L4171.6,7992L4168,7988.1L4155,7976L4152,7972.9L4137.1,7960L4136,7958.9L4120,7946L4117.1,7944L4104,7933.9L4094.7,7928L4088,7922.7L4072,7920L4056,7927.6L4055.4,7928L4040,7936.6L4029.6,7944L4024,7948.1L4010.3,7960L4008,7962.2L3995.2,7976L3992,7979.9L3982.8,7992L3976,8003L3973.7,8008L3972.3,8024L3975.7,8040L3976,8041.3L3979.2,8056L3982.7,8072L3986.3,8088L3989.9,8104L3992,8113.3L3993.6,8120L3997.4,8136L4001.4,8152L4005.3,8168L4008,8179L4009.4,8184L4013.7,8200L4018.1,8216L4022.4,8232L4024,8238L4027.1,8248L4032,8264L4038.1,8280L4040,8284L4056,8293.7L4060.5,8296L4072,8301.8L4088,8308.1L4101.6,8312L4104,8312.8L4120,8316.4L4136,8318.6L4152,8319.4L4168,8319L4184,8317.2L4200,8313.9L4206.6,8312ZM4153.8,9464L4168,9458.7L4184,9451L4189.2,9448L4200,9441.7L4213.8,9432L4216,9430.4L4232,9416.7L4232.8,9416L4247.9,9400L4248,9399.9L4260.3,9384L4264,9378.2L4270.4,9368L4278.2,9352L4280,9347.4L4284.6,9336L4289.4,9320L4292.5,9304L4294.2,9288L4294.6,9272L4293.7,9256L4291.5,9240L4287.7,9224L4282.3,9208L4280,9202.8L4275.4,9192L4266.6,9176L4264,9172.1L4255.7,9160L4248,9150.6L4242.2,9144L4232,9133.8L4225.4,9128L4216,9120.3L4204,9112L4200,9109.3L4184,9100.2L4174.9,9096L4168,9092.7L4152,9086.6L4136,9082L4126.2,9080L4120,9078.6L4104,9076L4088,9077.6L4085.1,9080L4072,9092.7L4069.2,9096L4056,9108.2L4052.4,9112L4040,9124.5L4037,9128L4024,9140.7L4020.9,9144L4008,9156.2L4004.2,9160L3992,9171.1L3986.7,9176L3976,9185.5L3968.4,9192L3960,9199.3L3949.4,9208L3944,9212.6L3929.6,9224L3928,9225.4L3912,9237.6L3908.5,9240L3896,9249.5L3886.2,9256L3880,9261L3864,9271.9L3863.8,9272L3854.3,9288L3855.7,9304L3858.7,9320L3863.4,9336L3864,9337.7L3869.2,9352L3877.1,9368L3880,9372.9L3886.7,9384L3896,9396.4L3898.9,9400L3912,9414.2L3913.8,9416L3928,9428.6L3932.5,9432L3944,9440.4L3956.8,9448L3960,9449.9L3976,9457.9L3991.8,9464L3992,9464.1L4008,9469.4L4024,9473.3L4040,9476L4056,9477.5L4072,9478L4088,9477.6L4104,9476.1L4120,9473.6L4136,9469.8L4152,9464.7L4153.8,9464Z","label":[4104.6,8686.7]},"3:VIII":{"path":"M5039.4,8648L5048,8642.4L5061,8632L5064,8629.3L5076.6,8616L5080,8611.7L5088.5,8600L5096,8590.3L5100.6,8584L5108.4,8568L5112,8558.5L5114.5,8552L5121.7,8536L5126.3,8520L5128,8515.4L5132.4,8504L5137.3,8488L5142.6,8472L5144,8468.3L5149,8456L5159,8440L5160,8438.2L5168.4,8424L5176,8411.7L5178.4,8408L5190.1,8392L5192,8389.5L5201.8,8376L5208,8366.8L5212.6,8360L5222.6,8344L5224,8341.6L5232.2,8328L5240,8312.9L5240.5,8312L5248.6,8296L5255.1,8280L5256,8277.5L5261.4,8264L5266.7,8248L5270.9,8232L5272,8226.7L5274.7,8216L5278,8200L5280.4,8184L5282.2,8168L5283.2,8152L5283.7,8136L5283.6,8120L5282.8,8104L5281.4,8088L5279.3,8072L5276.3,8056L5272.4,8040L5272,8038.8L5268.2,8024L5263.1,8008L5256.4,7992L5256,7991.1L5249.5,7976L5240.8,7960L5240,7958.7L5231.3,7944L5224,7933.7L5219.9,7928L5208,7913.5L5206.7,7912L5192,7896.5L5191.4,7896L5176,7882.3L5173,7880L5160,7869.9L5151,7864L5144,7859.4L5128,7850.5L5122.6,7848L5112,7843L5096,7837L5080,7832.5L5077.7,7832L5064,7828.2L5048,7825.1L5032,7823.1L5016,7822.2L5000,7822.2L4984,7823.3L4968,7825.4L4952,7828.6L4940,7832L4936,7832.9L4920,7837.7L4904,7844L4895.8,7848L4888,7851.6L4872,7860.8L4867.3,7864L4856,7871.5L4845.1,7880L4840,7884L4826.5,7896L4824,7898.4L4812.4,7912L4813.4,7928L4814.9,7944L4816.2,7960L4817.4,7976L4818.4,7992L4819.2,8008L4819.8,8024L4820.2,8040L4820.4,8056L4820.3,8072L4820,8088L4819.6,8104L4818.9,8120L4817.9,8136L4816.8,8152L4815.3,8168L4813.8,8184L4812.8,8200L4811.7,8216L4810.9,8232L4810.6,8248L4811.7,8264L4813.9,8280L4818,8296L4824,8311.6L4824.1,8312L4831.7,8328L4840,8342.3L4841,8344L4851.1,8360L4856,8367.2L4861.8,8376L4872,8390.8L4872.8,8392L4883.4,8408L4888,8415.9L4892.8,8424L4901.4,8440L4904,8444.8L4910.4,8456L4917.1,8472L4920,8479.4L4923.7,8488L4930.1,8504L4936,8519.3L4936.3,8520L4942.4,8536L4948.6,8552L4952,8561.4L4955,8568L4961.9,8584L4968,8596.7L4970,8600L4978.8,8616L4984,8625.9L4988.2,8632L4998.6,8648L5000,8650.3L5016,8660.1L5032,8652.5L5039.4,8648ZM4984.9,9736L5000,9734.3L5016,9731.7L5032,9728L5048,9723.2L5056.4,9720L5064,9717L5080,9709.4L5089.1,9704L5096,9700.3L5112,9689.8L5114.4,9688L5128,9676.8L5133.1,9672L5144,9660.9L5148.4,9656L5160,9641.3L5161,9640L5171.8,9624L5176,9616.5L5180.9,9608L5188.4,9592L5192,9582.7L5194.8,9576L5200.3,9560L5204.7,9544L5208,9528.1L5208,9528L5211.2,9512L5213.6,9496L5215.3,9480L5216.3,9464L5216.9,9448L5216.8,9432L5216.2,9416L5215,9400L5213.1,9384L5210.4,9368L5208,9357.2L5207,9352L5203.1,9336L5198,9320L5192,9305.1L5191.6,9304L5184.5,9288L5176,9272.7L5175.6,9272L5165.6,9256L5160,9248.5L5153.4,9240L5144,9229.3L5138.9,9224L5128,9213.6L5121.4,9208L5112,9200.9L5097.9,9192L5096,9190.7L5080,9181.3L5068.4,9176L5064,9173.9L5048,9167.8L5032,9163.3L5016,9160.2L5014.6,9160L5000,9158L4997.9,9160L4984,9168.5L4974.8,9176L4968,9180.9L4954.7,9192L4952,9193.8L4936,9206.2L4933.8,9208L4920,9218.9L4913.9,9224L4904,9231.5L4893.4,9240L4888,9244L4872.2,9256L4872,9256.2L4856,9267.4L4849.1,9272L4840,9278.5L4825.9,9288L4824,9289.3L4808,9299.7L4800.7,9304L4792,9309.4L4776,9318.4L4772.7,9320L4760,9327.4L4744,9335.8L4743.4,9336L4728,9344.1L4713.8,9352L4712,9355.8L4706.5,9368L4700.5,9384L4696,9399.1L4695.7,9400L4691.3,9416L4687.9,9432L4685.7,9448L4684.3,9464L4683.9,9480L4684.4,9496L4685.9,9512L4688.4,9528L4692,9544L4696,9556.7L4696.9,9560L4702.5,9576L4709.8,9592L4712,9596L4718.3,9608L4728,9623L4728.6,9624L4740.5,9640L4744,9644.2L4754.6,9656L4760,9661.5L4771.4,9672L4776,9676L4791.9,9688L4792,9688.1L4808,9698.5L4818.5,9704L4824,9707.1L4840,9714.9L4853.3,9720L4856,9721.1L4872,9726.5L4888,9730.5L4904,9733.5L4920,9735.6L4925.1,9736L4936,9737.1L4952,9737.8L4968,9737.5L4984,9736.1L4984.9,9736Z","label":[4977.3,8663.6]},"3:IV":{"path":"M2631.5,8568L2632,8567.7L2647.7,8552L2648,8551.7L2663.7,8536L2664,8535.8L2680,8521.3L2681.4,8520L2696,8506.4L2698.4,8504L2712,8493.5L2718.7,8488L2728,8480.5L2738.3,8472L2744,8467.7L2759.5,8456L2760,8455.7L2776,8445L2783.8,8440L2792,8435L2808,8425.7L2811.3,8424L2824,8417.2L2840,8409L2842.2,8408L2856,8401.5L2872,8394.4L2878.5,8392L2888,8388L2899.6,8376L2904,8367.6L2907.9,8360L2914.9,8344L2920,8329.7L2920.7,8328L2926.5,8312L2931.2,8296L2934.9,8280L2936,8273.7L2937.9,8264L2940.4,8248L2942,8232L2943,8216L2943.2,8200L2942.8,8184L2941.6,8168L2939.6,8152L2936.7,8136L2936,8132.8L2933.5,8120L2929.5,8104L2924.4,8088L2920,8076.6L2918.7,8072L2913.4,8056L2907.1,8040L2904,8032.9L2900.4,8024L2893.2,8008L2888,7997.9L2884.9,7992L2875.4,7976L2872,7970.8L2865.7,7960L2856,7945.6L2855,7944L2843.8,7928L2840,7922.9L2831.7,7912L2824,7902.6L2818.6,7896L2808,7884.2L2804.1,7880L2792,7866.8L2789.3,7864L2776,7850.5L2773.4,7848L2760,7836.5L2754.2,7832L2744,7822.9L2735.5,7816L2728,7809.9L2714.1,7800L2712,7798.6L2696,7789.2L2685.3,7784L2680,7780.9L2664,7772.8L2651.9,7768L2648,7766.4L2632,7760.8L2616,7756.6L2600,7753.5L2589,7752L2584,7751.1L2568,7749.5L2552,7749L2536,7749.8L2520,7751.7L2518.7,7752L2504,7754.3L2488,7757.9L2472,7762.8L2458.9,7768L2456,7769.1L2440,7776.4L2426.8,7784L2424,7785.6L2408,7796.2L2403.1,7800L2392,7809.1L2384.6,7816L2376,7824.5L2369.1,7832L2360,7842.5L2355.5,7848L2344,7864L2344,7864.1L2333.4,7880L2328,7889.6L2324.3,7896L2316.1,7912L2312,7921.2L2308.8,7928L2302.1,7944L2296.7,7960L2296,7962.3L2291.2,7976L2286.6,7992L2282.7,8008L2280,8021.8L2279.5,8024L2276.6,8040L2274.4,8056L2272.8,8072L2271.8,8088L2271.3,8104L2271.5,8120L2272.2,8136L2273.6,8152L2275.8,8168L2278.7,8184L2280,8189.8L2282,8200L2286,8216L2290.8,8232L2296,8246.4L2296.4,8248L2301.3,8264L2306.9,8280L2312,8292.8L2313.2,8296L2320.1,8312L2327.6,8328L2328,8328.9L2334.2,8344L2341.7,8360L2344,8364.4L2349.8,8376L2358.1,8392L2360,8395.5L2366.4,8408L2375.9,8424L2376,8424.2L2385.6,8440L2392,8448.9L2397.1,8456L2408,8470.6L2409,8472L2422.3,8488L2424,8489.6L2440,8503L2441.3,8504L2456,8518L2458.4,8520L2472,8530.7L2480,8536L2488,8541.4L2504,8550.3L2507.6,8552L2520,8558.1L2536,8564.1L2549.5,8568L2552,8568.7L2568,8572.1L2584,8574.3L2600,8575.5L2616,8575.7L2631.5,8568Z","label":[2595.5,8155.7]},"3:III":{"path":"M2859.4,9736L2872,9731.6L2888,9724.5L2896.2,9720L2904,9715.7L2920,9705L2921.3,9704L2936,9692.5L2941,9688L2952,9677.6L2957.4,9672L2968,9660.6L2972,9656L2984,9641.7L2985.4,9640L2996.7,9624L3000,9618.7L3006.8,9608L3015.7,9592L3016,9591.5L3024.4,9576L3031.6,9560L3032,9559L3038.9,9544L3045.1,9528L3048,9519.7L3051,9512L3056.4,9496L3060.9,9480L3064,9466.8L3064.8,9464L3069.1,9448L3072.6,9432L3075.7,9416L3078,9400L3079.9,9384L3080,9382.4L3081.5,9368L3082.6,9352L3083.3,9336L3083.5,9320L3083.3,9304L3082.7,9288L3081.8,9272L3080.5,9256L3080,9251.6L3079,9240L3077.3,9224L3075.4,9208L3073.1,9192L3070.6,9176L3067.7,9160L3064.5,9144L3064,9141.9L3061.4,9128L3058,9112L3053.9,9096L3049.6,9080L3048,9075L3044.9,9064L3039.7,9048L3033.4,9032L3032,9028.5L3027.2,9016L3020.2,9000L3016,8991.8L3012.2,8984L3004.4,8968L3000,8958.9L2996.6,8952L2989.2,8936L2984,8923.8L2982.4,8920L2976.4,8904L2973.2,8888L2972.1,8872L2972.6,8856L2975.5,8840L2979.3,8824L2983.3,8808L2984,8805.3L2987.4,8792L2990.8,8776L2993.4,8760L2995.2,8744L2995.7,8728L2995.1,8712L2993.3,8696L2989.7,8680L2985.4,8664L2984,8659.8L2980.1,8648L2973.6,8632L2968,8620.1L2966.1,8616L2958.3,8600L2952,8587.7L2950.2,8584L2942.6,8568L2936,8552.6L2935.7,8552L2930.2,8536L2925.7,8520L2922.1,8504L2920,8492.6L2919.2,8488L2916.7,8472L2914.2,8456L2911.3,8440L2907.6,8424L2904,8411.5L2903,8408L2895.2,8392L2888,8388L2878.5,8392L2872,8394.4L2856,8401.5L2842.2,8408L2840,8409L2824,8417.2L2811.3,8424L2808,8425.7L2792,8435L2783.8,8440L2776,8445L2760,8455.7L2759.5,8456L2744,8467.7L2738.3,8472L2728,8480.5L2718.7,8488L2712,8493.5L2698.4,8504L2696,8506.4L2681.4,8520L2680,8521.3L2664,8535.8L2663.7,8536L2648,8551.7L2647.7,8552L2632,8567.7L2631.6,8568L2626.5,8584L2632,8596.9L2633.3,8600L2638.9,8616L2643.6,8632L2647.3,8648L2648,8652.1L2649.9,8664L2652.1,8680L2653.3,8696L2655,8712L2657,8728L2659.5,8744L2662.6,8760L2664,8770.8L2664.7,8776L2668.6,8792L2670.7,8808L2672.2,8824L2672.4,8840L2670.7,8856L2664.9,8872L2664,8873.9L2657.2,8888L2648,8902.7L2647.2,8904L2633.7,8920L2632,8922L2620.6,8936L2616,8941.4L2607.3,8952L2600,8961.1L2594.6,8968L2584,8981.4L2582,8984L2570.4,9000L2568,9003.4L2559.3,9016L2552,9028.6L2550,9032L2541,9048L2536,9058.7L2533.3,9064L2525.8,9080L2520,9095.1L2519.6,9096L2513.2,9112L2507.7,9128L2504,9140.3L2502.7,9144L2497.6,9160L2493.2,9176L2489.3,9192L2488,9197.7L2485.2,9208L2481.4,9224L2478,9240L2475,9256L2472.5,9272L2472,9275.4L2469.9,9288L2467.7,9304L2466,9320L2464.7,9336L2464,9352L2463.7,9368L2463.9,9384L2464.6,9400L2465.9,9416L2467.9,9432L2470.5,9448L2472,9455.4L2473.5,9464L2477,9480L2481.3,9496L2486.8,9512L2488,9515L2492.3,9528L2498.7,9544L2504,9555.2L2506.1,9560L2513.9,9576L2520,9586.6L2523,9592L2533,9608L2536,9612.4L2543.9,9624L2552,9634.5L2556.3,9640L2568,9653.1L2570.7,9656L2584,9669.4L2586.8,9672L2600,9684.1L2604.7,9688L2616,9697.1L2625.9,9704L2632,9708.1L2648,9717.3L2653.6,9720L2664,9725.6L2680,9732.5L2690.3,9736L2696,9738.1L2712,9742.7L2728,9746.2L2744,9748.6L2760,9750L2776,9750.6L2792,9750.2L2808,9748.8L2824,9746.3L2840,9742.6L2856,9737.4L2859.4,9736Z","label":[2770,9223.4]},"3:X":{"path":"M4028.2,8920L4040,8917.3L4056,8911.2L4069.6,8904L4072,8902.9L4088,8893.1L4094.8,8888L4104,8881L4113.9,8872L4120,8866L4128.9,8856L4136,8846.7L4140.7,8840L4149.9,8824L4152,8819.1L4156.7,8808L4161.9,8792L4165.2,8776L4166.7,8760L4166.6,8744L4164.8,8728L4161.3,8712L4155.7,8696L4152,8688L4148.1,8680L4138,8664L4136,8661.4L4124.6,8648L4120,8643.3L4106.7,8632L4104,8629.9L4088,8619.7L4080.3,8616L4072,8612L4056,8606.5L4040,8602.9L4024,8601.1L4008,8601L3992,8602.5L3976,8605.7L3960,8610.8L3948.6,8616L3944,8618.1L3928,8627.8L3922.3,8632L3912,8640.5L3904.3,8648L3896,8657.6L3891,8664L3880.9,8680L3880,8681.8L3873.2,8696L3867.8,8712L3864.3,8728L3864,8730.5L3862.4,8744L3862.3,8760L3863.9,8776L3864,8776.4L3867.1,8792L3872.3,8808L3878.2,8824L3880,8827.5L3886.8,8840L3896,8853.7L3897.7,8856L3911,8872L3912,8873.1L3927.5,8888L3928,8888.5L3944,8901.1L3949,8904L3960,8911.2L3976,8918L3984.6,8920L3992,8922.2L4008,8923.4L4024,8921.3L4028.2,8920ZM3886.2,9256L3896,9249.5L3908.5,9240L3912,9237.6L3928,9225.4L3929.6,9224L3944,9212.6L3949.4,9208L3960,9199.3L3968.4,9192L3976,9185.5L3986.7,9176L3992,9171.1L4004.2,9160L4008,9156.2L4020.9,9144L4024,9140.7L4037,9128L4040,9124.5L4052.4,9112L4056,9108.2L4069.2,9096L4072,9092.7L4085.1,9080L4081.2,9064L4072,9053.6L4066.2,9048L4056,9038.4L4047.4,9032L4040,9026L4024,9016.7L4022.2,9016L4008,9009.2L3992,9005.2L3976,9004.3L3960,9006L3944,9010.2L3930,9016L3928,9016.7L3912,9024.3L3899.7,9032L3896,9034.2L3880,9046.1L3877.8,9048L3864,9060.7L3860.8,9064L3848,9079.3L3847.5,9080L3836.9,9096L3832,9105.9L3829.1,9112L3822.8,9128L3818.5,9144L3816.1,9160L3816,9161.1L3815.2,9176L3816,9191.4L3816,9192L3818.5,9208L3822.7,9224L3829,9240L3832,9245.8L3837.4,9256L3848,9271.2L3864,9271.9L3880,9261L3886.2,9256ZM4069.1,10264L4072,10263.5L4088,10259.5L4104,10254L4117.3,10248L4120,10247L4136,10239.4L4148.1,10232L4152,10229.6L4168,10217.7L4170.1,10216L4184,10203.8L4187.9,10200L4200,10188.4L4204.3,10184L4216,10169.8L4217.4,10168L4228.7,10152L4232,10146.6L4238.6,10136L4246.9,10120L4248,10117.6L4254.7,10104L4261.3,10088L4264,10080.2L4267.2,10072L4272.5,10056L4276.9,10040L4280,10026L4280.5,10024L4284.3,10008L4287.4,9992L4289.9,9976L4291.9,9960L4293.4,9944L4294.5,9928L4295.1,9912L4295.4,9896L4295.2,9880L4294.5,9864L4293.3,9848L4291.5,9832L4289,9816L4285.7,9800L4281.4,9784L4280,9779.7L4276.8,9768L4271.3,9752L4264.4,9736L4264,9735.3L4257.1,9720L4248.2,9704L4248,9703.7L4238.7,9688L4232,9678.6L4227.2,9672L4216,9658L4214.3,9656L4200,9640.5L4199.5,9640L4184,9625.4L4182.3,9624L4168,9612.5L4161.3,9608L4152,9601.7L4136,9592.8L4134.3,9592L4120,9584.4L4104,9577.9L4098.1,9576L4088,9572.3L4072,9567.9L4056,9564.9L4040,9563L4024,9562.1L4008,9562.3L3995.9,9576L3992,9581.2L3986.1,9592L3976,9606.8L3975.4,9608L3965.3,9624L3960,9631.6L3955.3,9640L3945.1,9656L3944,9657.5L3935.1,9672L3928,9682.5L3924.7,9688L3914.4,9704L3912,9707.5L3904,9720L3896,9731.8L3893.2,9736L3882.3,9752L3880,9755.4L3871.1,9768L3864,9778.3L3859.8,9784L3848.2,9800L3848,9800.3L3836,9816L3832,9821.6L3823.4,9832L3816,9842L3810.6,9848L3800,9861.4L3797.4,9864L3784,9880L3783.9,9880L3769.5,9896L3768,9898.1L3754.6,9912L3752,9918.7L3747.9,9928L3749.2,9944L3751.1,9960L3752,9965.7L3753.3,9976L3755.7,9992L3758.7,10008L3762.4,10024L3766.8,10040L3768,10043.7L3771.4,10056L3776.6,10072L3783,10088L3784,10090.1L3789.8,10104L3797.7,10120L3800,10124.1L3806.2,10136L3816,10151.2L3816.5,10152L3827.6,10168L3832,10173.4L3840.9,10184L3848,10191.3L3857.3,10200L3864,10206.4L3875.1,10216L3880,10220L3896,10231.3L3897.1,10232L3912,10240.8L3927.9,10248L3928,10248.1L3944,10255.1L3960,10260.3L3975.7,10264L3976,10264.1L3992,10267.1L4008,10268.9L4024,10269.3L4040,10268.6L4056,10266.7L4069.1,10264Z","label":[4008,9733.8]}},"courseBoxes":{"1":[260,260,3834,4139.1],"2":[2420,4839.1,5095.3,6542.7],"3":[2469.1,7242.7,5046.2,10075.4],"L":[4534,260,7255.2,3512.2]}}