A note on intermediate differentiability of Lipschitz functions
Zajíček, Luděk
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 795-799 / Harvested from 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.

Publié le : 1999-01-01
Classification:  46G05,  58C20 
@article{119133,
     author = {Lud\v ek Zaj\'\i \v cek},
     title = {A note on intermediate differentiability of Lipschitz functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {795-799},
     zbl = {1010.46042},
     mrnumber = {1756555},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119133}
}

Zajíček, Luděk. A note on intermediate differentiability of Lipschitz functions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 795-799. http://gdmltest.u-ga.fr/item/119133/

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