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萨尔德定理

Sard's theorem

theorem that the set of the critical values of a smooth function has measure zero

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 values 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.

摘自英文维基百科「Sard's theorem」(英文维基百科,暂无中文条目),CC BY-SA 4.0

类型
定理
命名来源
Anthony Morse、Arthur Sard
属于
数学定理列表
研究学科
微积分
学科
数学

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