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.

References in corpus (1)

• Porosities and dimensions of measures

Cited by in corpus (11)

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• Rectifiability of pointwise doubling measures in Hilbert Space
• Cones, rectifiability, and singular integral operators
• Dynamics of the scenery flow and conical density theorems
• Local conical dimensions for measures
• Porosity in conformal dynamical systems
• A kind of local strong one-side porosity