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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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Article copyright: © Copyright 1979 American Mathematical Society

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