Locally Lipschitz functions are generically pseudo-regular on separable Banach spaces

Abstract

For a locally Lipschitz function on a separable Banach space the set of points of Gâteaux differentiability is dense but not necessarily residual. However, the set of points where the upper Dini derivative and the Clarke derivative agree is residual. It follows immediately that the set of points of intermediate differentiability is also residual and the set of points where the function is Gâteaux but not strictly differentiable is of the first category.