A note on a corollary of Sard's theorem
Author: John C. Wells
Journal: Proc. Amer. Math. Soc. 48 (1975), 513-514
MSC: Primary 26A63; Secondary 28A75
MathSciNet review: 0364578
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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.
-  John W. Milnor, Topology from the differentiable viewpoint, Based on notes by David W. Weaver, The University Press of Virginia, Charlottesville, Va., 1965. MR 0226651
-  Arthur Sard, The measure of the critical values of differentiable maps, Bull. Amer. Math. Soc. 48 (1942), 883–890. MR 0007523, https://doi.org/10.1090/S0002-9904-1942-07811-6