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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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 $\Omega = {\Omega _1} \times \cdots \times {\Omega _n}(n > 1)$ be a product of $n$ Brelot harmonic spaces each of which has a bounded potential, and let $K$ be a compact subset of $\Omega$. Then, $K$ is an $n$-polar set with the property that every $i$-section $(1 \leqslant i < n)$ of $K$ through any point in $\Omega$ is $(n - i)$ polar if and only if every positive continuous function on $K$ can be extended to a continuous potential on $\Omega$. Further, it has been shown that if $f$ is a nonnegative continuus function on $\Omega$ with compact support, then $MRf$, the multireduced function of $f$ over $\Omega$, is also a continuous function on $\Omega$.


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Article copyright: © Copyright 1987 American Mathematical Society