Upper porous measures on metric spaces
type: Item
instance of: scholarly article
title: Upper porous measures on metric spaces
zbMATH Open document ID: 1183.28009
author: Ville Suomala
published in: Illinois Journal of Mathematics
publication date: 2009-10-15T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1254403725
review text: The porosity of a measure at a point on a metric space indicates how large, as measured by radius, balls of relatively small measure can be relative to balls centered at the point in question. Proper formulations, too lengthy to reproduce here, involve limits of suprema of numbers with the right property. The author is concerned with a variation called upper porosity and gives a technical sufficient condition for a measure to be upper porous. In Euclidean spaces upper porosity is equivalent to having lower conical density zero at almost all points. The paper closed with an example of a Hausdorff measure on \([0,1]\) that is not upper porous.
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 5615679
zbMATH Keywords: upper porous measure
zbMATH Keywords: packing measure
zbMATH Keywords: Hausdorff measure
reviewed by: K. P. Hart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5615679