Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces
type: Item
instance of: scholarly article
title: Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces
zbMATH Open document ID: 1203.31018
DOI: 10.4171/RMI/598
author: Anders Björn
author: Jana Björn
author: Mikko Parviainen
published in: Revista Matemática Iberoamericana
publication date: 2010-05-17T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1266330121
review text: The authors provide a new proof for the fundamental convergence theorem for superharmonic functions on metric measure spaces. The theorem states that a regularized infimum of superharmonic functions is a superharmonic function. They also provide a new proof for the fact that Newtonian functions have Lebesgue points outside a set of capacity zero, and give a sharp result on when superharmonic functions have \(L^q\)-Lebesgue points everywhere.
reviewed by: Riikka Korte
Mathematics Subject Classification ID: 31E05
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 5708819
zbMATH Keywords: \(\mathcal{A}\)-harmonic function
zbMATH Keywords: \(p\)-harmonic function
zbMATH Keywords: superharmonic function
zbMATH Keywords: fundamental convergence theorem
Wikidata QID: Q110086166
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5708819