A compact convex set with no extreme points

Extreme Points of the Convex Set of Joint Probability Distributions with Fixed Marginals

By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.

Extreme Points of Polar Convex Sets

A Compact Convex Set in £3 Whose Exposed Points Are of the First Category

Extreme convex set functions with many nonnegative differences

Where N is a nite set of the cardinality n and P the family of all its subsets, we study real functions on P having nonnegative diierences of orders n?2, n?1 and n. Nonnegative diierences of zeroth order, rst order, and second order may be interpreted as nonnegativity, nonincreasingness and convexity, respectively. If all diierences up to order n of a function are nonnegative, the set function ...

On the Chvátal-Gomory Closure of a Compact Convex Set

In this paper, we show that the Chvátal-Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver [17] for irrational polytopes1, and generalizes the same result for the case of rational polytopes [17], rational ellipsoids [8] and strictly convex bodies [7].