Continuous functions on multipolar sets

Author:
Ramasamy Jesuraj

Journal:
Proc. Amer. Math. Soc. **99** (1987), 331-339

MSC:
Primary 31D05

DOI:
https://doi.org/10.1090/S0002-9939-1987-0870796-7

MathSciNet review:
870796

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Abstract: Let be a product of Brelot harmonic spaces each of which has a bounded potential, and let be a compact subset of . Then, is an -polar set with the property that every -section of through any point in is polar if and only if every positive continuous function on can be extended to a continuous potential on . Further, it has been shown that if is a nonnegative continuus function on with compact support, then , the multireduced function of over , is also a continuous function on .

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0870796-7

Article copyright:
© Copyright 1987
American Mathematical Society