Abstract
The main result of the article is
Theorem 1. Let v: Ω → ℝ be a C1-smooth function on a domain Ω → ℝ2. Suppose that 0 ∉ Cl Int Dv(Ω). Then the measure of the image of the set of critical points equals zero.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 1083–1091, September–October, 2006.
Original Russian Text Copyright © 2006 Korobkov M. V.
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Korobkov, M.V. An analog of Sard’s theorem for C 1-smooth functions of two variables. Sib Math J 47, 889–895 (2006). https://doi.org/10.1007/s11202-006-0098-2
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DOI: https://doi.org/10.1007/s11202-006-0098-2