A note on a corollary of Sard's theorem
John C. Wells
Proc. Amer. Math. Soc. 48 (1975), 513-514
Primary 26A63; Secondary 28A75
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Abstract: A corollary of Sard's theorem is the following:
Corollary. Let be a smooth (i.e. ) map defined on a compact subset of . Let . Then the Lebesgue measure of is zero.
The purpose of this note is to show that a similar version of this theorem holds for Lipschitz functions.
W. Milnor, Topology from the differentiable viewpoint, Based
on notes by David W. Weaver, The University Press of Virginia,
Charlottesville, Va., 1965. MR 0226651
Sard, The measure of the critical values of
differentiable maps, Bull. Amer. Math. Soc.
883–890. MR 0007523
- John Milnor, Topology from the differential viewpoint, Univ. Press of Virginia, Charlottesville, Va., 1965. MR 37 #2239. MR 0226651 (37:2239)
- A. Sard, The measure of the critical values of differential maps, Bull. Amer. Math. Soc. 48 (1942), 883-890. MR 4, 153. MR 0007523 (4:153c)
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