Conical upper density theorems and porosity of measures

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.

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-01
Main Authors: Käenmäki, Antti, Suomala, Ville
Format: Article
Language:English
Subjects:
Density
Porosity
Theorems
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1701.08587