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Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1238-6751
Helsinki University Technology.
2010 (English)In: REVISTA MATEMATICA IBEROAMERICANA, ISSN 0213-2230, Vol. 26, no 1, 147-174 p.Article in journal (Refereed) Published
Abstract [en]

We prove the nonlinear fundamental convergence theorem for superharmonic functions on metric measure spaces. Our proof seems to be new even in the Euclidean setting. The proof uses direct methods in the calculus of variations and, in particular, avoids advanced tools from potential theory. We also provide a new proof for the fact that a Newtonian function has Lebesgue points outside a set of capacity zero, and give a sharp result on when superharmonic functions have L-q-Lebesgue points everywhere.

Place, publisher, year, edition, pages
Revista Matematika -- Iberoamericana-spain , 2010. Vol. 26, no 1, 147-174 p.
Keyword [en]
A-harmonic, fundamental convergence theorem, Lebesgue point, metric space, Newtonian function, nonlinear, p-harmonic, quasicontinuous, Sobolev function, superharmonic, superminimizer, supersolution, weak upper gradient
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-57163DOI: 10.4171/RMI/598ISI: 000278145200007OAI: oai:DiVA.org:liu-57163DiVA: diva2:323562
Available from: 2010-06-11 Created: 2010-06-11 Last updated: 2016-05-04

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Björn, AndersBjörn, Jana

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