Titlebook: Classical Potential Theory and Its Probabilistic Counterpart; Advanced Problems J. L. Doob Book 1984 Springer-Verlag New York Inc. 1984 Mar

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https://doi.org/10.1007/978-1-4757-3425-6The class of relative harmonic functions is suggested by the following trivial remark. Let (., .) be a measurable space, and suppose that to each point ξ of . is assigned some set (perhaps empty) . of probability measures on ..

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Introduction to the Mathematical Background of Classical Potential TheoryIn this chapter some of the mathematical ideas of classical potential theory are introduced, under simplifying assumptions. The basic space is Euclidean . space ℝ.. For a ball . in ℝ..

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Basic Properties of Harmonic, Subharmonic, and Superharmonic FunctionsLet . and if . denote by . the image of ξ under inversion in ∂.. That is, . is on the ray from ξ. through ξ, and .. To simplify the notation take ..

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