Symmetric function kernels and sweeping of measures
  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. 
Bent Fuglede
math.CA