Abstract
It is shown that any convex combination of harmonic meaures corresponding to a finite family of open neighborhoods of the given point x can be approximated by a sequence of harmonic measures corresponding to a sequence of open neighborhoods of x in the union of the given family. This solves an open problem raised in connection with Jensen measures by B.J.Cole and T.J.
Ransford. It is also proved that, for every Green domain X containing x, the extremal representing measures for x with respect to the convex cone of potentials on X are dense in the compact convex set of all representing measures.
Results are presented simultaneously for the classical potential theory and for the theory of Riesz potentials. Also, very general potential-theoretic setting covering a wide class of second order PDE´s.