Singular Sets of Uniformly Asymptotically Doubling Measures

Abstract

In the following paper, we prove a dimension bound on the singular set of a Radon measure assuming its doubling ratio converges uniformly on compact sets. More precisely, we prove that if a Radon measure is $n$-Uniformly Asymptotically Doubling, then $\dim ({\mathcal{S}}_{\mu })\le n-3$, where ${\mathcal{S}}_{\mu }$ is the singular set of the measure.

arXiv admin note: text overlap with arXiv:1510.03732

References in corpus (2)

• Uniform measures and uniform rectifiability
• A sharp bound on the Hausdorff dimension of the singular set of an n-uniform measure