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On intermediate differentiability of Lipschitz functions on certain Banach spaces


Authors: M. Fabián and D. Preiss
Journal: Proc. Amer. Math. Soc. 113 (1991), 733-740
MSC: Primary 46G05; Secondary 26E15, 46B20, 58C20
DOI: https://doi.org/10.1090/S0002-9939-1991-1074753-0
MathSciNet review: 1074753
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Abstract: A real-valued function $ f$ defined on a Banach space $ X$ is said to be intermediately differentiable at $ x \in X$ if there is $ \xi \in {X^*}$ such that for every $ h \in X$ the value $ \left\langle {\xi ,h} \right\rangle $ lies between the upper and lower derivatives of $ f$ at $ x$ in the direction $ h$. We show that if $ Y$ contains a dense continuous linear image of an Asplund space and $ X$ is a subspace of $ Y$, then every locally Lipschitz function on $ X$ is generically intermediately differentiable.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1074753-0
Keywords: Lipschitz function, upper, lower, and intermediate derivative, Asplund space, dentability
Article copyright: © Copyright 1991 American Mathematical Society

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