Abstract
A polar of ℝN is a set to each point of which corresponds an open neighborhood of the point that carries a superharmonic function equal to + ∞ at each point of the set in the neighborhood. An inner polar 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 transforms are also.
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© 1984 Springer-Verlag New York Inc.
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Doob, J.L. (1984). Polar Sets and Their Applications. In: Classical Potential Theory and Its Probabilistic Counterpart. Grundlehren der mathematischen Wissenschaften, vol 262. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5208-5_5
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DOI: https://doi.org/10.1007/978-1-4612-5208-5_5
Publisher Name: Springer, New York, NY
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