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

Departament de Matemàtiques

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

6 Cites (Scopus)

Resum

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.

Idioma original	Anglès
Pàgines (de-a)	217-227
Revista	Advances in Mathematics
Volum	242
DOIs	https://doi.org/10.1016/j.aim.2013.03.024
Estat de la publicació	Publicada - 1 d’ag. 2013

Accés al document

10.1016/j.aim.2013.03.024

Altres arxius i enllaços

https://www.scopus.com/pages/publications/84877892761

Com citar-ho

@article{5a41c5818edd4d73a4ff9bdd72a55b95,

title = "The Morse-Sard theorem for Clarke critical values",

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. {\textcopyright} 2013 Elsevier Ltd.",

keywords = "Cantor-Bendixson derivative, Clarke critical value, Lipschitz function, Morse-Sard theorem",

author = "Luc Barbet and Marc Dambrine and Aris Daniilidis",

year = "2013",

month = aug,

day = "1",

doi = "10.1016/j.aim.2013.03.024",

language = "English",

volume = "242",

pages = "217--227",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - The Morse-Sard theorem for Clarke critical values

AU - Barbet, Luc

AU - Dambrine, Marc

AU - Daniilidis, Aris

PY - 2013/8/1

Y1 - 2013/8/1

N2 - 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.

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.

KW - Cantor-Bendixson derivative

KW - Clarke critical value

KW - Lipschitz function

KW - Morse-Sard theorem

UR - https://www.scopus.com/pages/publications/84877892761

U2 - 10.1016/j.aim.2013.03.024

DO - 10.1016/j.aim.2013.03.024

M3 - Article

SN - 0001-8708

VL - 242

SP - 217

EP - 227

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The Morse-Sard theorem for Clarke critical values

Resum

Accés al document

Altres arxius i enllaços

Fingerprint

Com citar-ho