Level set

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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. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098