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

Open Access


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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Copyright information

© The Author(s) 2018

Authors and Affiliations

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

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