arXiv:1408.5892 Abstract | arXiv Analytics

arXiv:1408.5892 [math.FA]Abstract References Reviews Resources

Capacities and Hausdorff measures on metric spaces

Published 2014-08-25Version 1

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 $h(t)=\log^{1-Q-\epsilon}(1/t).$

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

Categories: math.FA

Subjects: 31C15, 28A78

Keywords: metric spaces, hausdorff measures, capacity zero, poincare inequality, chain condition

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