GATEAUX DIFFERENTIABILITY OF CONE-MONOTONE AND POINTWISE LIPSCHITZ FUNCTIONS

We give a geometric description of the smallest sigma-ideal (C) over tilde of subsets of a separable Banach space with respect to which cone-monotone functions are Gateaux 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 Gateaux and Hadamard differentiability of functions with values in spaces with the Radon-Nikodym property, hold with the exceptional sets belonging to (C) over tilde.