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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Generic differentiability of Lipschitzian functions


Author: G. Lebourg
Journal: Trans. Amer. Math. Soc. 256 (1979), 125-144
MSC: Primary 58C20; Secondary 26A16
MathSciNet review: 546911
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Abstract: It is shown that, in separable topological vector spaces which are Baire spaces, the usual properties that have been introduced to study the local ``first order'' behaviour of real-valued functions which satisfy a Lipschitz type condition are ``generically'' equivalent and thus lead to a unique class of ``generically smooth'' functions.

These functions are characterized in terms of tangent cones and directional derivatives and their ``generic'' differentiability properties are studied. The results extend some of the well-known differentiability properties of continuous convex functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0546911-1
PII: S 0002-9947(1979)0546911-1
Article copyright: © Copyright 1979 American Mathematical Society