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Journal d'Analyse Mathématique

, Volume 135, Issue 1, pp 59–83 | Cite as

The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces

  • Anders Björn
  • Jana Björn
  • Visa Latvala
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Abstract

We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. We apply these key tools to establish a fine version of the Kellogg property, characterize finely continuous functions by means of quasicontinuous functions, and show that capacitary measures associated with Cheeger supersolutions are supported by the fine boundary of the set.

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Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Department of MathematicsLinköpings Universitet LinköpingSweden
  2. 2.Department of Physics and MathematicsUniversity of Eastern FinlandJoensuuFinland

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