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A new proof of Fréchet differentiability of Lipschitz functions

Joram LindenstraussDavid Preiss — 2000

Journal of the European Mathematical Society

We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on 2 (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.

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