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Title: A note on intermediate differentiability of Lipschitz functions (English)
Author: Zajíček, Luděk
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 40
Issue: 4
Year: 1999
Pages: 795-799
Category: math
Summary: 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. (English)
Keyword: Lipschitz function
Keyword: intermediate derivative
Keyword: $\sigma$-porous set
Keyword: superreflexive Banach space
MSC: 46G05
MSC: 58C20
idZBL: Zbl 1010.46042
idMR: MR1756555
Date available: 2009-01-08T18:57:47Z
Last updated: 2012-04-30
Stable URL:
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