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FRÉCHET INTERMEDIATE DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS ON ASPLUND SPACES

Part of: Existence theories

Published online by Cambridge University Press:  13 March 2009

J. R. GILES
J. R. GILES*
Affiliation:
University of Newcastle, NSW 2308, Australia (email: John.Giles@newcastle.edu.au)
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Abstract

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The deep Preiss theorem states that a Lipschitz function on a nonempty open subset of an Asplund space is densely Fréchet differentiable. However, the simpler Fabian–Preiss lemma implies that it is Fréchet intermediately differentiable on a dense subset and that for a large class of Lipschitz functions this dense subset is residual. Results are presented for Asplund generated spaces.

Keywords

Lipschitz functionsFréchet differentiabilityAsplund and Asplund generated spaces

MSC classification

Secondary: 49J52: Nonsmooth analysis
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 309 - 317
Copyright
Copyright © Australian Mathematical Society 2009

References

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