Stability of convex sets and applications

M. E. Shirokov

Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 840-856.

Résumé

We briefly review the results related to the notion of stability of convex sets and consider some of their applications. We prove a corollary of the stability property which enables us to develop an approximation technique for concave functions on a wide class of convex sets. This technique yields necessary and sufficient conditions for the local continuity of concave functions. We describe some examples of their applications.

Détail

Keywords: stable convex set, concave function, weak convergence of probability measures
Mots-clés : barycentric map.

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