Conical upper density theorems and porosity of measures

Abstract

We study how measures with finite lower density are distributed around $(n-m)$-planes in small balls in ${\mathbb{R}}^n$. We also discuss relations between conical upper density theorems and porosity. Our results may be applied to a large collection of Hausdorff and packing type measures.

Cited by in corpus (5)

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• Directed porosity on conformal iterated function systems and weak convergence of singular integrals
• On upper conical density results
• Rectifiability of pointwise doubling measures in Hilbert Space
• A kind of local strong one-side porosity