Sard’s theorem


Let U be an open set in Rm, V be an open set in Rn and f:UV be a Ck functionMathworldPlanetmath. If km/n, then the set of critical values of f has n-dimensional measure zeroMathworldPlanetmath.


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