论文标题
措施的分化是完整的Riemannian歧管
Differentiation of measures on complete Riemannian manifolds
论文作者
论文摘要
在本说明中，我们给出了\ cite {eg1992}给出的besicovitch覆盖理论版本的新证明结果，我们证明了$（m，g）$的borel措施的差异化定理，它为radon-nikodym的密度提供了两个非负局部局部有限的borel borel的公式。
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 $ν_1, ν_2$ on $(M, g)$ such that $ν_1 \ll ν_2$, extending the known case when $(M, g)$ is a standard Euclidean space.
