Abstract

This paper describes a class of convex closed sets, S, in RnR^n 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 RnR^n having this property are generalized polyhedral convex sets. In particular, the only compact convex sets in RnR^n having this property are polytopes.

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Keywords

  • Polyhedral convex sets
  • correspondence
  • locally convex sets

Mathematics Subject Classification

52B99

References

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Suggested citation

F. Hüsseinov. “A Characterization of Polyhedral Convex Sets.” Journal of Convex Analysis 11 (2004), No. 1, 245–250. https://doi.org/10.68381/jca11016

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Published by Heldermann Verlag, 2004. Rights now held by Banach Press.