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Locally Lipschitz functions are generically pseudo-regular on separable Banach spaces

Published online by Cambridge University Press:  17 April 2009

J.R. Giles  and
Scott Sciffer
J.R. Giles
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia
Scott Sciffer
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia
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Abstract

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For a locally Lipschitz function on a separable Banach space the set of points of Gâteaux differentiability is dense but not necessarily residual. However, the set of points where the upper Dini derivative and the Clarke derivative agree is residual. It follows immediately that the set of points of intermediate differentiability is also residual and the set of points where the function is Gâteaux but not strictly differentiable is of the first category.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 205 - 212
Copyright
Copyright © Australian Mathematical Society 1993

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