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Sard's theorem
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{{Short description|Theorem in mathematical analysis}} In [[mathematics]], '''Sard's theorem''', also known as '''Sard's lemma''' or the '''Morse–Sard theorem''', is a result in [[mathematical analysis]] that asserts that the set of [[critical value (critical point)|critical value]]s (that is, the [[image (mathematics)|image]] of the set of [[critical point (mathematics)|critical point]]s) of a [[smooth function]] ''f'' from one [[Euclidean space]] or [[manifold]] to another is a [[null set]], i.e., it has [[Lebesgue measure]] 0. This makes the set of critical values "small" in the sense of a [[generic property]]. The theorem is named for [[Anthony Morse]] and [[Arthur Sard]].
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