The dimension of weakly mean porous measures: a probabilistic approach
type: Item
instance of: scholarly article
zbMATH Open document ID: 1294.28007
author: Pablo Shmerkin
publication date: 2012-06-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.1394
full work available at URL: porosityprob.pdf
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 6042733
zbMATH Keywords: Porosity
zbMATH Keywords: mean porous measure
zbMATH Keywords: the packing dimension
MaRDI profile type: Publication
OpenAlex ID: W2964233035
arXiv ID: 1010.1394
DOI: 10.1093/IMRN/RNR085
published in: IMRN. International Mathematics Research Notices
title: The dimension of weakly mean porous measures: a probabilistic approach
review text: Using probabilistic ideas, we prove that if \(\mu \) is a mean porous measure on \(\mathbb R^n\), then the packing dimension of \(\mu \) is strictly smaller than n. Moreover, we give an explicit bound for the packing dimension, which is asymptotically sharp in the case of small porosity. This result was stated in [\textit{D. B. Beliaev} and \textit{S. K. Smirnov}, ``On dimension of porous measures'', Math. Ann. 323, No. 1, 123--141 (2002; Zbl 1037.28003)], but the proof given there is not correct. We also give estimates on the dimension of weakly mean porous measures, which improve another result of Beliaev and Smirnov.
description: scientific article; zbMATH DE number 6042733