A characterization of polyhedral convex sets
Journal of Convex Analysis
245 - 250
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This paper describes a class of convex closed sets, S, in Rn for which the following property holds: for every correspondence defined on a probability space with relative open values in S its integral is a relative open subset of S. It turns out, that the only closed convex sets in R n having this property are generalized polyhedral convex sets. In particular, the only compact convex sets in Rn having this property are polytopes.