Null sets and essentially smooth Lipschitz functions

被引：19

作者：

Borwein, JM ^{[1
]}

Moors, WB

机构：

[1] Simon Fraser Univ, Dept Math & Stat, CECM, Burnaby, BC V5A 1S6, Canada

[2] Univ Auckland, Dept Math, Auckland, New Zealand

来源：

SIAM JOURNAL ON OPTIMIZATION | 1998年 / 8卷 / 02期

关键词：

Lipschitz functions; Haar-null sets; essentially smooth functions;

D O I：

10.1137/S1052623496305213

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：309 / 323

页数：15