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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on a corollary of Sard’s theorem
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by John C. Wells PDF
Proc. Amer. Math. Soc. 48 (1975), 513-514 Request permission

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.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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