At its core, continuity implies that small changes in the input of a function result in small changes in its output. More ...

Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

A necessary and sufficient condition is given that a semicontinuous, nonnegative, concave function on a finite dimensional closed convex set $X$ necessarily be ...