Geodesic
A Characterization of Polyhedral Convex Sets
Journal of convex analysis, Tome 11 (2004) no. 1, pp. 245-25.

Voir la notice de l'article provenant de la source Heldermann Verlag

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 Rn having this property are generalized polyhedral convex sets. In particular, the only compact convex sets in Rn having this property are polytopes.
Classification : 52B99
Mots-clés : Polyhedral convex sets, correspondence, locally convex sets 
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     author = {F. H\"usseinov},
     title = {A {Characterization} of {Polyhedral} {Convex} {Sets}},
     journal = {Journal of convex analysis},
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     number = {1},
     year = {2004},
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F. Hüsseinov. A Characterization of Polyhedral Convex Sets. Journal of convex analysis, Tome 11 (2004) no. 1, pp. 245-25. http://geodesic.mathdoc.fr/item/JCA_2004_11_1_JCA_2004_11_1_a15/