Capacities and Hausdorff measures on metric spaces

2014/08/25 by Karak, Nijjwal, Koskela, Pekka
#28A78 #31C15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1408.5892

Abstract

In this article, we show that in a Q-doubling space (X,d,μ), Q>1, that supports a Q-Poincaré inequality and satisfies a chain condition, sets of Q-capacity zero have generalized Hausdorff h-measure zero for h(t)=log^1-Q-ε(1/t).

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