  It is shown that, for open sets in classical potential theory and - more
generally - for elliptic harmonic spaces, the set of Jensen measures for a
point is a simple union of closed faces of a compact convex set which has been
thoroughly studied a long time ago. In particular, the set of extreme Jensen
measures can be immediately identified. The results hold even without
ellipticity (thus capturing also many examples for the heat equation) provided
a rather weak approximation property for superharmonic functions or a certain
transience property holds.
