Symmetric function kernels and sweeping of measures

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.