Every closed convex set is the set of minimizers of some <i>C</i>∞-smooth convex function

作     者：Azagra, D Ferrera, J 

作者机构：Univ Complutense Dept Anal Matem Fac Ciencias Matem E-28040 Madrid Spain 

出 版 物：《PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY》 (美国数学会会报)

年 卷 期：2002年第130卷第12期

页      面：3687-3692页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Banach-spaces Convex function Convexity Banach space Set 

摘      要：We show that for every closed convex set C in a separable Banach space X there is a C-infinity-smooth convex function f : X-- [0, infinity) so that f(-1) (0) = C. We also deduce some interesting consequences concerning smooth approximation of closed convex sets and continuous convex functions.