Let be a -mapping of manifolds and of dimensions and , respectively; if , then the critical values (cf. Critical value) of form a set of measure zero. The set of regular values turns out to be of full measure and everywhere dense. The theorem was proved by A. Sard .
|||A. Sard, "The measure of critical values of differentiable maps" Bull. Amer. Math. Soc. , 48 (1942) pp. 883–890|
"Full measure" is, in the Russian article, called "massive setmassive" . See also Singularities of differentiable mappings.
Sard theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sard_theorem&oldid=11998