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arXiv · 1401.2536

On a measure-theoretic area formula

Valentino Magnani
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Abstract

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.

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Valentino Magnani. 2020-12-26. On a measure-theoretic area formula. https://arxiv.org/abs/1401.2536

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