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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Infima of convex functions


Author: Gerald Beer
Journal: Trans. Amer. Math. Soc. 315 (1989), 849-859
MSC: Primary 90C25; Secondary 26B25, 49A50, 54C08, 90C48
MathSciNet review: 953536
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Abstract: Let $ \Gamma (X)$ be the lower semicontinuous, proper, convex functions on a real normed linear space $ X$. We produce a simple description of what is, essentially, the weakest topology on $ \Gamma (X)$ such that the value functional $ f \to \inf f$ is continuous on $ \Gamma (X)$. When $ X$ is reflexive, convergence of a sequence in this topology is equivalent to Mosco plus pointwise convergence of the corresponding sequence of conjugate convex functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0953536-9
PII: S 0002-9947(1989)0953536-9
Keywords: Convex function, value functional, minimization, Mosco convergence, conjugate convex function, affine topology
Article copyright: © Copyright 1989 American Mathematical Society