Abstract:By classical results of G.C. Evans and G. Choquet on "good" kernels G in potential theory, for every polar K σ -set P , there exists a finite measure μ on P such that its potential Gμ is infinite on P , and a set P admits a finite measure μ on P such that Gμ is infinite exactly on P if and only if P is a polar G δ -set. A known application of Evans' theorem yields the solutions of the generalized Dirichlet problem for open sets by the Perron-Wiener-Brelot method using only harmonic upper and lower functions. I… Show more
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