The Morse-Sard theorem for Clarke critical values

Luc Barbet; Marc Dambrine; Aris Daniilidis

doi:10.1016/j.aim.2013.03.024

The Morse-Sard theorem for Clarke critical values

Luc Barbet, Marc Dambrine, Aris Daniilidis

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

The Morse-Sard theorem states that the set of critical values of a Ck smooth function defined on a Euclidean space Rd has Lebesgue measure zero, provided k?d. This result is hereby extended for (generalized) critical values of continuous selections over a compactly indexed countable family of Ck functions: it is shown that these functions are Lipschitz continuous and the set of their Clarke critical values is null. © 2013 Elsevier Ltd.

Original language	English
Pages (from-to)	217-227
Journal	Advances in Mathematics
Volume	242
DOIs	https://doi.org/10.1016/j.aim.2013.03.024
Publication status	Published - 1 Aug 2013

Keywords

Cantor-Bendixson derivative
Clarke critical value
Lipschitz function
Morse-Sard theorem

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10.1016/j.aim.2013.03.024

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AB - The Morse-Sard theorem states that the set of critical values of a Ck smooth function defined on a Euclidean space Rd has Lebesgue measure zero, provided k?d. This result is hereby extended for (generalized) critical values of continuous selections over a compactly indexed countable family of Ck functions: it is shown that these functions are Lipschitz continuous and the set of their Clarke critical values is null. © 2013 Elsevier Ltd.

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KW - Lipschitz function

KW - Morse-Sard theorem

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JF - Advances in Mathematics

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The Morse-Sard theorem for Clarke critical values

Abstract

Keywords

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