A criterion of Gamma-nullness and differentiability of convex and quasiconvex functions

Abstract

We introduce a criterion for a set to be Gamma-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Frechet differentiable is Gamma-null.

Our criterion also implies a new result about Gateaux (and Hadamard) differentiability of quasiconvex functions.

Keywords

• differentiability
• Gamma-null sets
• convex function
• quasiconvex function