The Morse-Sard theorem for Clarke critical values

Luc Barbet, Marc Dambrine, Aris Daniilidis

Research output: Contribution to journalArticleResearchpeer-review

3 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 languageEnglish
Pages (from-to)217-227
JournalAdvances in Mathematics
Volume242
DOIs
Publication statusPublished - 1 Aug 2013

Keywords

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

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