Potential Analysis

, Volume 34, Issue 1, pp 81-88

First online:

Coincidence of Harmonic and Finely Harmonic Functions

  • Stephen J. GardinerAffiliated withSchool of Mathematical Sciences, University College Dublin Email author 

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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 function Fine topology Finely harmonic function Baire category

Mathematics Subject Classification (2010)