Capacities and Hausdorff measures on metric spaces

Published 25 Aug 2014 in math.FA | (1408.5892v1)

Abstract: In this article, we show that in a $Q$-doubling space $(X,d,\mu),$ $Q>1,$ that supports a $Q$-Poincar\'e inequality and satisfies a chain condition, sets of $Q$-capacity zero have generalized Hausdorff $h$-measure zero for $h(t)=\log^{{1-Q-\epsilon}(1/t).$}

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