We prove that action of a semigroup T on compact metric space X by continuous
selfmaps is strongly proximal if and only if T action on P(X), the space of
probability measures on $X$ with weak topology, is strongly proximal. As a
consequence we prove that affine actions on certain compact convex subsets of
finite-dimensional vector spaces are strongly proximal if and only if the
action is proximal.Comment: 6pages. to appear in Archivum Math. (Brno) (2003