Maßeinheiten (Länge, Flächeninhalt, Volumen etc.) berechnen

Das Maß einer Region entspricht der Länge einer Kurve, dem Flächeninhalt einer Fläche und dem Volumen eines Körpers. Es kann jedoch sowohl auf nulldimensionale Objekte verallgemeinert werden, für die das Maß abzählbar ist, als auch auf -dimensionale Objekte, deren Maß ein verallgemeinertes Volumen ist. Bei einer Region, die Elemente unterschiedlicher Dimensionen enthält, wird das Maß auf Basis der maximalen Dimension ermittelt und wird gegeben durch das Integral , wobei die Region ist.

Kurvenlängen:

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Flächeninhalt der Flächen:

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Volumen von geometrischen Körpern:

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