Generalising generic differentiability properties from convex to locally Lipschitz functions (Q1343972)

This paper aims at generalizing the generic differentiability results of \textit{D. Preiss, R. R. Phelps} and \textit{I. Namioka} [Isr. J. Math. 72, No. 3, 257-279 (1990; Zbl 0757.46028)] and \textit{R. R. Phelps} [``Convex functions, monotone operators and differentiability'', Lect. Notes Math. 1364, Berlin (1989)] for convex functions on Asplund spaces to locally Lipschitz functions. It is shown that such a function is fully and uniformly intermediately differentiable on a dense \(G_\delta\)-subset. Moreover, the set of points, where the subdifferential is weak\(^*\) norm lower semi-continuous is also a \(G_\delta\)-subset.