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Sard's theorem (Theorem)
Theorem 1   Let $U$ be an open set in $R^m$ $V$ be an open set in $R^n$ and $f: U \to V$ be a $C^k$ function. If $k \geq m/n$ then the set of critical values of $f$ has $n$ dimensional measure zero.

Bibliography

1
S.G. Krantz, H. R. Parks, The Implicit Function Theorem: History, Theory, and Applications, Birkhäuser, Boston, c. 2002
2
H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969




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Cross-references: measure zero, critical values, function, open set

This is version 4 of Sard's theorem, born on 2006-08-31, modified 2006-10-06.
Object id is 8305, canonical name is SardsTheorem2.
Accessed 1234 times total.

Classification:
AMS MSC57R35 (Manifolds and cell complexes :: Differential topology :: Differentiable mappings)

Pending Errata and Addenda
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