Upper porosity with respect to measures
type: Item
instance of: scholarly article
title: Upper porosity with respect to measures
zbMATH Open document ID: 1246.28003
author: Martin Koc
published in: Real Analysis Exchange
publication date: 2012-05-10T00:00:00Z
reviewed by: Enrico Zoli
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 6032476
zbMATH Keywords: upper porosity
zbMATH Keywords: generalized upper porosity
zbMATH Keywords: upper porosity of measures
MaRDI profile type: Publication
full work available at URL: realanalexch.36.1.0091
OpenAlex ID: W1564636624
DOI: 10.14321/REALANALEXCH.36.1.0091
review text: Let \(X\) be a separable metric space and \(\mu\) a Borel regular probability measure on \(X\). The author defines the notion of \(\mu\)-upper porosity for subsets of \(X\), thus generalizing the concept of upper porosity of \(\mu\) introduced by \textit{M. E. Mera} and \textit{M. Morán} [Real Anal. Exch. 26, No. 1, 101--115 (2001; Zbl 1023.28002)].NEWLINENEWLINEMore general types of \(\mu\)-upper porosity with respect to suitable porosity functions are explored. Finally, using ideas and results from [\textit{M. E. Mera, M. Morán, D. Preiss} and \textit{L. Zajíček}, Nonlinearity 16, No. 1, 247--255 (2003; Zbl 1026.28001)], several decomposition theorems for \(\mu\)-upper porous sets are proved.
description: scientific article; zbMATH DE number 6032476