Noncompact simplexes in Banach spaces with the Radon-Nikodým property

It is well known that a compact convex subset C of a locally convex topological vector space is a simplex if and only if each point x of C admits a unique probability measure on the extreme points of C with barycenter x. An exact analog of this result is proved for a closed and bounded separable convex subset of a Banach space with the Radon-Nikodým Property, and a weaker analog is proved in the nonseparable case.