Geodesic
Stability of convex sets and applications
Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 840-856

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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.
Keywords: stable convex set, concave function, weak convergence of probability measures
Mots-clés : barycentric map. 
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     author = {M. E. Shirokov},
     title = {Stability of convex sets and applications},
     journal = {Izvestiya. Mathematics },
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     number = {4},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_4_a7/}
}
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M. E. Shirokov. Stability of convex sets and applications. Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 840-856. http://geodesic.mathdoc.fr/item/IM2_2012_76_4_a7/