Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on a corollary of Sard’s theorem


Author: John C. Wells
Journal: Proc. Amer. Math. Soc. 48 (1975), 513-514
MSC: Primary 26A63; Secondary 28A75
DOI: https://doi.org/10.1090/S0002-9939-1975-0364578-4
MathSciNet review: 0364578
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A corollary of Sard’s theorem is the following: Corollary. Let $f:K \to {R^n}$ be a smooth (i.e. $f \in {C^k},k \geq 1$) map defined on a compact subset $K$ of ${R^n}$. Let $C = \{ y|{f^{ - 1}}(y)\;is\;infinite\}$. Then the Lebesgue measure of $C$ is zero. The purpose of this note is to show that a similar version of this theorem holds for Lipschitz functions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A63, 28A75

Retrieve articles in all journals with MSC: 26A63, 28A75


Additional Information

Article copyright: © Copyright 1975 American Mathematical Society