Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces
2010 (English)In: REVISTA MATEMATICA IBEROAMERICANA, ISSN 0213-2230, Vol. 26, no 1, 147-174 p.Article in journal (Refereed) Published
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.
A-harmonic, fundamental convergence theorem, Lebesgue point, metric space, Newtonian function, nonlinear, p-harmonic, quasicontinuous, Sobolev function, superharmonic, superminimizer, supersolution, weak upper gradient
IdentifiersURN: urn:nbn:se:liu:diva-57163DOI: 10.4171/RMI/598ISI: 000278145200007OAI: oai:DiVA.org:liu-57163DiVA: diva2:323562