The Morse Sard theorem for Clarke critical values
Abstract The Morse Sard theorem states that the set of critical values of a C k smooth function defined on a Euclidean space R d 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 C k functions: it is shown that these functions are Lipschitz continuous and the set of their Clarke critical values is null.