Title

A necessary and sufficient condition on the stability of the infimum of convex functions

Document Type

Article

Publication Date

2019

Department

Department of Mathematical Sciences

Abstract

Let us say that a convex function f : C → [−∞, ∞] on a convex set C ⊆ R is infimum-stable if, for any sequence (fn) of convex functions fn : C → [−∞, ∞] converging to f pointwise, one has inf C fn → inf C f. A simple necessary and sufficient condition for a convex function to be infimumstable is given. The same condition remains necessary and sufficient if one uses Moore-Smith nets (fν) in place of sequences (fn). This note is motivated by certain applications to stability of measures of risk/inequality in finance/economics.

Publication Title

Journal of Convex Analysis

Share

COinS