The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces
Self archived versionpublished version
MetadataShow full item record
CitationBjörn, Anders. Björn, Jana. Latvala, Visa. (2018). The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces. Journal d'Analyse Mathématique, 135 (1) , 59–83. 10.1007/s11854-018-0029-8.
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.