Null Sets and Essentially Smooth Lipschitz Functions

In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are...

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Bibliographic Details
Published inSIAM journal on optimization Vol. 8; no. 2; pp. 309 - 323
Main Authors Borwein, Jonathan M., Moors, Warren B.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.05.1998
Subjects
Algebra
Applied mathematics
Banach spaces
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Summary:In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623496305213