Potential Analysis

, Volume 34, Issue 1, pp 81–88

Coincidence of Harmonic and Finely Harmonic Functions


DOI: 10.1007/s11118-010-9182-0

Cite this article as:
Gardiner, S.J. Potential Anal (2011) 34: 81. doi:10.1007/s11118-010-9182-0


This paper answers an old question of Fuglede by characterising those finely open sets U with the following property: any finely harmonic function on U must coincide with a harmonic function on some non-empty finely open subset.


Harmonic functionFine topologyFinely harmonic functionBaire category

Mathematics Subject Classification (2010)


Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College DublinDublin 4Ireland