The generalized Morse-Sard theorem

被引：0
|
作者：
McLennan, Andrew [1 ]
机构：
[1] Univ Queensland, Sch Econ, Level 6 Colin Clark Bldg, St Lucia, Qld 4072, Australia
来源：
EXPOSITIONES MATHEMATICAE | 2021年 / 39卷 / 04期
关键词：
Morse-Sard theorem; Hausdorff measure; Holder continuity; Whitney extension theorem; LUZIN N-PROPERTY; SMOOTHNESS HYPOTHESIS; IMAGES; PROOF; SET;
D O I：
10.1016/j.exmath.2021.01.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Morse-Sard theorem gives conditions under which the set of critical values of a function between Euclidean spaces has Lebesgue measure zero. Over the years the result has been extended and strengthened in various ways. We present a result, along with a simple proof, that subsumes many of these generalizations. We also review methods of constructing examples showing that differentiability hypotheses cannot be weakened, and we construct a complete set of examples for our result. (C) 2021 Elsevier GmbH. All rights reserved.
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页码：515 / 539
页数：25
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