Calculus of Variations and Geometric Measure Theory

V. Magnani

On a measure-theoretic area formula

created by magnani on 09 Jan 2014
modified on 13 Jan 2021


Published Paper

Inserted: 9 jan 2014
Last Updated: 13 jan 2021

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 145
Pages: 885-891
Year: 2015


We show how classical differentiation theorems for measures can be turned into an integral representation of a Borel measure with respect to a fixed Carathéodory measure. We focus our attention on the cases where this measure is both the Hausdorff measure and the spherical Hausdorff measure, giving the corresponding measure-theoretic area formula. Our point consists in using certain covering derivatives as "generalized densities". Some consequences for the sub-Riemannian Heisenberg group are also pointed out.

Tags: GeMeThNES