NULL SETS AND ESSENTIALLY SMOOTH LIPSCHITZ FUNCTIONS

Authors
BORWEIN JM MOORS WB
Citation
Jm. Borwein et Wb. Moors, NULL SETS AND ESSENTIALLY SMOOTH LIPSCHITZ FUNCTIONS, SIAM journal on optimization, 8(2), 1998, pp. 309-323
Citations number
21
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on optimization → ACNP
ISSN journal
10526234
Volume
8
Issue
2
Year of publication
1998
Pages
309 - 323
Database
ISI
SICI code
1052-6234(1998)8:2<309:NSAESL>2.0.ZU;2-Y
Abstract
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 essen tially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.