Infima of convex functions

Beer, Gerald

doi:10.1090/S0002-9947-1989-0953536-9

Infima of convex functions
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Trans. Amer. Math. Soc. 315 (1989), 849-859 Request permission

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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Duality for the sum of convex functions in general Banach spaces

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