Three convex sets
Author: Michel Talagrand
Journal: Proc. Amer. Math. Soc. 89 (1983), 601-607
MSC: Primary 46A55
MathSciNet review: 718981
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Abstract: We construct a Choquet simplex such that there is a universally measurable affine function on , which satisfies the barycentric calculus, and is zero on the set of extreme points, but is not identically zero. We also construct a closed convex bounded set of a Banach space without extreme points, but such that each point is the barycenter of a maximal measure. Finally, we construct a closed bounded set of and a maximal measure on which is supported by a weak Baire set which contains no extreme points.
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