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Functions Harmonic on a Ball
Boundary Limit Theorems
12 other sections not shown
assume balayage ball Borel measurable Borel set Borel subsets boundary function compact closure compact set compact subset compact support component Consider constant continuous function continuous second partials converges Corollary countable da(z definition denote Dirichlet problem easily seen equation finite a.e. function G GB(x GR(x greatest harmonic minorant Green function h is harmonic harmonic function If/is increasing sequence inequality Kelvin transform Lebesgue measure lim inf lim inf,,_x lim sup limit point measurable function minimum principle neighborhood open subset polar set polar subset positive harmonic function positive integer positive numbers positive superharmonic function potential theory preceding lemma preceding theorem Proof prove regular boundary point relative resolutive signed measure subharmonic subset of dR super-mean-valued Suppose thin topology uniformly x e dR zero