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A noncompact Choquet theorem


Author: G. A. Edgar
Journal: Proc. Amer. Math. Soc. 49 (1975), 354-358
MSC: Primary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1975-0372586-2
MathSciNet review: 0372586
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372586-2
Keywords: Choquet's theorem, Radon-Nikodým property, extreme measure, vector-valued martingale
Article copyright: © Copyright 1975 American Mathematical Society

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