Sard theorem

From Encyclopedia of Mathematics
Revision as of 16:57, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 [1].


[1] 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.

How to Cite This Entry:
Sard theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article