  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.
