Continuous functions on multipolar sets

Ramasamy Jesuraj
1987 Proceedings of the American Mathematical Society  
Let Ü = Q1 x ■ ■ ■ X Q" (n > 1) be a product of n Brelot harmonic spaces each of which has a bounded potential, and let A" be a compact subset of Ü. Then, K is an «-polar set with the property that every /-section (1 ^ i < n) of K through any point in £2 is (n -/) polar if and only if every positive continuous function on K can be extended to a continuous potential on Ü. Further, it has been shown that if / is a nonnegative continuus function on Q with compact support, then MRf, the
more » ... Rf, the multireduced function of / over ß, is also a continuous function on Q.
doi:10.1090/s0002-9939-1987-0870796-7 fatcat:asdipymr7reh3db4dlueyhza7i