# Level set

From Encyclopedia of Mathematics

*of a function *

The set of points in on which . If the function is given on a square of the plane and has partial derivatives there which also satisfy a Lipschitz condition, then for almost-all in the interval the level set

consists of a finite number of regular curves (on them, ). Cf. Sard theorem.

**How to Cite This Entry:**

Level set.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Level_set&oldid=18462

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article