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