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 \(h(t)=\log ^{1-Q-\epsilon }(1/t)\).
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This work was supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (Grant no. 271983) and also via Grant No. 131477.
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Karak, N., Koskela, P. Capacities and Hausdorff measures on metric spaces. Rev Mat Complut 28, 733–740 (2015). https://doi.org/10.1007/s13163-015-0174-x
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DOI: https://doi.org/10.1007/s13163-015-0174-x