On the mean value property of finely harmonic and finely hyperharmonic functions
type: Item
instance of: scholarly article
title: On the mean value property of finely harmonic and finely hyperharmonic functions
zbMATH Open document ID: 0709.31002
DOI: 10.1007/BF01833150
published in: Aequationes Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137351
review text: Let U be a bounded finely open set in \({\mathbb{R}}^ 2\) and let \(\tilde U\) denote its fine closure. It is shown that, if f is finely lower semicontinuous on \(\tilde U\) and finely hyperharmonic on U, then f(x)\(\geq \int_{*}f d\epsilon_ x^{CV}\) for any finely open set V with \(\tilde V\subseteq U\). (Here \(\epsilon_ x^{CV}\) denotes fine harmonic measure for V). An example is given to demonstrate that this result fails in \({\mathbb{R}}^ n\) when \(n\geq 3\).
Mathematics Subject Classification ID: 31A99
Mathematics Subject Classification ID: 31C40
Mathematics Subject Classification ID: 31B99
zbMATH DE Number: 4165284
zbMATH Keywords: mean value property
zbMATH Keywords: finely hyperharmonic function
zbMATH Keywords: fine harmonic measure
reviewed by: Stephen J. Gardiner
MaRDI profile type: Publication
cites work: Finely harmonic functions
cites work: Fonctions harmoniques et fonctions finement harmoniques
cites work: Sur les fonctions finement holomorphes
cites work: Fine hyperharmonicity without axiom D
cites work: Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions
OpenAlex ID: W1997327423
author: Bent Fuglede
description: scientific article; zbMATH DE number 4165284