Revista Matemática Complutense

, Volume 28, Issue 3, pp 733–740 | Cite as

Capacities and Hausdorff measures on metric spaces

  • Nijjwal Karak
  • Pekka Koskela


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


Capacity Generalized Hausdorff measure Poincaré inequality 

Mathematics Subject Classification

31C15 28A78 


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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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