A criterion of $\varGamma $-nullness and differentiability of convex and quasiconvex functions
Volume 227 / 2015
Studia Mathematica 227 (2015), 149-164
MSC: Primary 46G05; Secondary 49J50.
DOI: 10.4064/sm227-2-5
Abstract
We introduce a criterion for a set to be $\varGamma $-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 Fréchet differentiable is $\varGamma $-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.
