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arXiv · 1605.08660

Symmetric function kernels and sweeping of measures

Bent Fuglede
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Abstract

This is a potential theoretic study of balayage (sweeping) of a positive Radon measure on a locally compact (Hausdorff) space onto a closed, or more generally a quasiclosed set (that is, a set which can be approximated in outer capacity by closed sets). The setting is that of potentials with respect to a suitable positive symmetric function kernel. Following Choquet (1959) we consider energy capacity, not as a set function, but as a functional, acting on positive numerical functions. The finiteness of the upper capacity of the potential restricted to the set in question is sufficient for the possibility of the sweeping.

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Bent Fuglede. 2016-05-27. Symmetric function kernels and sweeping of measures. https://arxiv.org/abs/1605.08660

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