Geodesic
A note on intermediate differentiability of Lipschitz functions
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 795-799 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46G05, 58C20
Keywords: Lipschitz function; intermediate derivative; $\sigma$-porous set; superreflexive Banach space 
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     author = {Zaj{\'\i}\v{c}ek, Lud\v{e}k},
     title = {A note on intermediate differentiability of {Lipschitz} functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {795--799},
     year = {1999},
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     number = {4},
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     zbl = {1010.46042},
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Zajíček, Luděk. A note on intermediate differentiability of Lipschitz functions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 795-799. http://geodesic.mathdoc.fr/item/CMUC_1999_40_4_a16/