  Let us say that a convex function f\colon C\to[-\infty,\infty] on a convex
set C\subseteq\R is infimum-stable if, for any sequence (f_n) of convex
functions f_n\colon C\to[-\infty,\infty] converging to f pointwise, one has
\inf_C f_n\to\inf_C f. A simple necessary and sufficient condition for a convex
function to be infimum-stable is given. The same condition remains necessary
and sufficient if one uses Moore--Smith nets (f_\nu) in place of sequences
(f_n). This note is motivated by certain applications to stability of measures
of risk/inequality in finance/economics.
