Sard’s theorem

Theorem.

Let $U$ be an open set in $R^m$, $V$ be an open set in $R^n$ and $f\mathrm{:}U\mathrm{\to }V$ be a $C^k$ function. If $k\mathrm{\ge }m\mathrm{/}n$, then the set of critical values of $f$ has $n$-dimensional measure zero.

Title	Sard’s theorem
Canonical name	SardsTheorem
Date of creation	2013-03-22 16:12:33
Last modified on	2013-03-22 16:12:33
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	7
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 57R35