On dimension of porous measures

D. B. Beliaev, S. K. Smirnov

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

We introduce a notion of mean porosity for measures and obtain dimensional bounds for mean-porous and porous measures. As a corollary we generalize to all porous Borel measures the estimate obtained recently by J.-P. Eckmann, E. Järvenpää, and M. Järvenpää for porous measures satisfying the doubling condition. We also discuss various generalizations of this notion and possible applications.

Original languageEnglish
Pages (from-to)123-141
Number of pages19
JournalMathematische Annalen
Volume323
Issue number1
DOIs
Publication statusPublished - 2002
Externally publishedYes

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