Satz von Sard

Sard's theorem In mathematics, Satz von Sard, 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 (das ist, the image of the set of critical points) of a smooth function f from one Euclidean space or manifold to another is a null set, d.h., it has Lebesgue measure 0. This makes the set of critical values "klein" in the sense of a generic property. The theorem is named for Anthony Morse and Arthur Sard.

Inhalt 1 Aussage 2 Variants 3 Siehe auch 4 Verweise 5 Further reading Statement More explicitly,[1] Lassen {displaystyle fcolon mathbb {R} ^{n}rightarrow mathbb {R} ^{m}} be {Anzeigestil C^{k}} , (das ist, {Anzeigestil k} times continuously differentiable), wo {displaystyle kgeq max{n-m+1,1}} . Lassen {displaystyle Xsubset mathbb {R} ^{n}} denote the critical set of {Anzeigestil f,} which is the set of points {displaystyle xin mathbb {R} ^{n}} at which the Jacobian matrix of {Anzeigestil f} Rang hat {Anzeigestil

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