Artículo de revista
The Morse–Sard theorem for Clarke critical values
Fecha
2013Registro en:
Advances in Mathematics 242 (2013) 217–227
DOI 10.1016/j.aim.2013.03.024
Autor
Barbet, Luc
Dambrine, Marc
Daniilidis, Aris
Institución
Resumen
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.