
Journal of Convex Analysis 11 (2004), No. 1, 245250 Copyright Heldermann Verlag 2004 A Characterization of Polyhedral Convex Sets Farhad Hüsseinov Dept. of Economics, Bilkent University, 06533 Ankara, Turkey, farhad@bilkent.edu.tr This paper describes a class of convex closed sets, S, in R^{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 R^{n} having this property are generalized polyhedral convex sets. In particular, the only compact convex sets in R^{n} having this property are polytopes. Keywords: Polyhedral convex sets, correspondence, locally convex sets. MSC: 52B99. FullTextpdf (239 KB) for subscribers only. 