The Zygmund Morse-Sard Theorem |
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Authors: | Alec Norton |
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Institution: | 1. Department of Mathematics, University of Texas at Austin, USA
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Abstract: | The classical Morse-Sard Theorem says that the set of critical values off:R n+k →R n has Lebesgue measure zero iff ∈C k+1. We show theC k+1 smoothness requirement can be weakened toC k+Zygmund. This is corollary to the following theorem: For integersn >m >r > 0, lets = (n ?r)/(m ?r); iff:R n →R m belongs to the Lipschitz class Λ s andE is a set of rankr forf, thenf(E) has measure zero. |
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