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Proceedings of the American Mathematical Society

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Continuous functions on polar sets

Author: Ramasamy Jesuraj
Journal: Proc. Amer. Math. Soc. 93 (1985), 262-266
MSC: Primary 31D05
MathSciNet review: 770533
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Abstract: Let $ \Omega $ be a second countable Brelot harmonic space with a positive potential. If $ K$ is a compact subset of $ \Omega $ with more than one point, then $ K$ is a polar set iff every positive continuous function on $ K$ can be extended to a continuous potential on $ \Omega = {{\mathbf{R}}^n}(n \geqslant 3)$. This is a generalization of the result proved by H. Wallin for the special case $ \Omega = {{\mathbf{R}}^n}(n \geqslant 3)$ with Laplace harmonic space.

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