2020/08/30 by Jürgen Jost, Jost, Jürgen, Hông Vân Lê +3
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2008.13252
openalex publication_date 2020/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we give a new proof of a version of the Besicovitch covering theorem, given in \citeEG1992, \citeBogachev2007 and extended in \citeFederer1969, 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 ν1, ν2 on (M, g) such that ν1 ≪ ν2, extending the known case when (M, g) is a standard Euclidean space.