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arXiv · 1408.5892

Capacities and Hausdorff measures on metric spaces

Nijjwal Karak·Pekka Koskela
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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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Nijjwal Karak, Pekka Koskela. 2014-08-25. Capacities and Hausdorff measures on metric spaces. https://arxiv.org/abs/1408.5892

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