## L. Zaj\'\i \v cek

*A note on intermediate differentiability of Lipschitz functions *

Comment.Math.Univ.Carolinae 40,4 (1999) 795-799. **Abstract:**Let $f$ be a Lipschitz function on a superreflexive Banach space $X$. We prove that then the set of points of $X$ at which $f$ has no intermediate derivative is not only a first category set (which was proved by M. Fabian and D. Preiss for much more general spaces $X$), but it is even $\sigma $-porous in a rather strong sense. In fact, we prove the result even for a stronger notion of uniform intermediate derivative which was defined by J.R. Giles and S. Sciffer.

**Keywords:** Lipschitz function, intermediate derivative, $\sigma $-porous set, superreflexive Banach space

**AMS Subject Classification:** Primary 46G05; Secondary 58C20

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