A new proof of Fréchet differentiability of Lipschitz functions

Abstract. We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on Ê2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w* closure of the set of its points of Gâteaux differentiability is norm separable.