Capacities and Hausdorff measures on metric spaces

Abstract

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

10 pages. arXiv admin note: substantial text overlap with arXiv:1408.5718