Lipschitz Functions with Maximal Clarke Subdifferentials Are Generic

. We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given. AMS (1991) subject classification: Primary 49J52. Secondary 26E25, 54E52. Key words: Lipschitz function, Clarke subdifferential, separable Banach spaces, Baire category, partial ordering, Banach lattice, approximate subdifferential. 1 Research supported by NSERC and the Shrum endowment of Simon Fraser University 1 Introduction and Definitions We shall be working in a separable Banach space E, with norm k \Delta k, whose topological dual is denoted by E and whose dual unit ball is denoted by B . For S ae E, a closed convex cone, the positive polar cone is defined by: S + := fx 2 E j hx ; si 0 for every s 2 Sg: Let A ae E be an open bounded convex set. Throughout f : A 7! R denotes a Lipschitz function an..