Gâteaux differentiability of cone-monotone and pointwise Lipschitz functions

Abstract

We give a geometric description of the smallest σ-ideal Open image in new window of subsets of a separable Banach space with respect to which cone-monotone functions are Gâteaux differentiable almost everywhere. We also show that the usual generalizations of Rademacher’s and Stepanov’s theorems for metric and weak*-differentiability, as well as for Gâteaux and Hadamard differentiability of functions with values in spaces with the Radon-Nikodym property, hold with the exceptional sets belonging to Open image in new window.