Area formula (geometric measure theory)
id:
area-formula-geometric-measure-theory-196-15820848
title:
Area formula (geometric measure theory)
text:
In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem. Definition: Given f : R n → R m and A ⊂ R n , the multiplicity function N , y ∈ R m , is the number of points in the preimage f − 1 ∩ A . The multiplicity function is also called the Banach
brand slug:
wiki
category slug:
encyclopedia
description:
Area formula from geometric measure theory
original url:
https://en.wikipedia.org/wiki/Area_formula_(geometric_measure_theory)
date created:
date modified:
2023-11-09T09:28:06Z
main entity:
{"identifier":"Q111914125","url":"https://www.wikidata.org/entity/Q111914125"}
image:
fields total:
13
integrity:
14