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Björn, Anders; Björn, Jana; Parviainen, Mikko

Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces. (English) Zbl 1203.31018

Rev. Mat. Iberoam. 26, No. 1, 147-174 (2010).
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.
Reviewer: Riikka Korte (Helsinki)

Cited in 17 Documents

MSC:

31E05 Potential theory on fractals and metric spaces
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
31C45 Other generalizations (nonlinear potential theory, etc.)
35J60 Nonlinear elliptic equations

Keywords:

\(\mathcal{A}\)-harmonic function; \(p\)-harmonic function; superharmonic function; fundamental convergence theorem
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\textit{A. Björn} et al., Rev. Mat. Iberoam. 26, No. 1, 147--174 (2010; Zbl 1203.31018)
Full Text: DOI Euclid

References:

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