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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Lattices and Related Classes of FunctionsIn this chapter certain function classes that arise naturally in potential theory will be discussed. These classes, the corresponding identically named classes in parabolic potential theory (Section XVIII.19) and in stochastic process theory (Chapter V of Part 2), are discussed together in Chapter I of Part 3.

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The Martin BoundaryLet . be an open subset of ℝ.. If . is a ball, its Euclidean boundary is so well adapted to it from a potential theoretic point of view that the following statements are true.

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https://doi.org/10.1007/0-8176-4444-Xt of the set in the neighborhood. An . set is a set whose compact subsets are polar. It will be shown in Section VI.2 that an analytic inner polar set is polar. If a set is (inner) polar its Kelvin transformsare also.

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Classification and Discrimination,n . is said to be . than .) if . ⊂ .. For any family of extended real-valued functions on a space there is a coarsest topology making every member of the family continuous, namely, the intersection of all the topologies doing this. The . topology of classical potential theory is defined as the coars

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https://doi.org/10.1007/978-1-4757-3803-2ductor, if . is a connected conducting body in ℝ., the charge on A distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in

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