A noncompact Choquet theorem

Edgar, G. A.

doi:10.1090/S0002-9939-1975-0372586-2

A noncompact Choquet theorem
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by G. A. Edgar PDF

Proc. Amer. Math. Soc. 49 (1975), 354-358 Request permission

Abstract:

The following noncompact analog of Choquet’s theorem is proved. Let $E$ be a Banach space with the Radon-Nikodým property, let $C$ be a separable, closed, bounded, convex subset of $E$, and let a be a point in $C$. Then there is a probability measure $\mu$ on the universally measurable sets in $C$ such that $a$ is the barycenter of $\mu$ and the set of extreme points of $C$ has $\mu$-measure 1.

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