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arXiv · 2008.13252

Differentiation of measures on complete Riemannian manifolds

Jürgen Jost·Hông Vân Lê·Tat Dat Tran
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Abstract

In this note we give a new proof of a version of the Besicovitch covering theorem, given in \cite{EG1992}, \cite{Bogachev2007} and extended in \cite{Federer1969}, for locally finite Borel measures on finite dimensional complete Riemannian manifolds $(M,g)$. As a consequence, we prove a differentiation theorem for Borel measures on $(M,g)$, which gives a formula for the Radon-Nikodym density of two nonnegative locally finite Borel measures $\nu_1, \nu_2$ on $(M, g)$ such that $\nu_1 \ll \nu_2$, extending the known case when $(M, g)$ is a standard Euclidean space.

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Jürgen Jost, Hông Vân Lê, Tat Dat Tran. 2020-08-30. Differentiation of measures on complete Riemannian manifolds. https://arxiv.org/abs/2008.13252

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