# On a measure theoretic area formula

created by magnani on 09 Jan 2014
modified on 04 Aug 2015

[BibTeX]

Published Paper

Inserted: 9 jan 2014
Last Updated: 4 aug 2015

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

Abstract:

We review some classical differentiation theorems for measures, showing how they can be turned into an integral representation of a Borel measure with respect to a fixed Carathe'odory measure. We focus our attention on the case this measure is the spherical Hausdorff measure, giving a metric measure 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