On the image size of singular maps. II
The author presents some new refinements of the well-known Morse-Sard theorem: If \(f\in C^ k(\mathbb{R}^ n,\mathbb{R}^ m)\) and \(k\geq \max\{n- m+1,1\}\), then the image of the critical set of \(f\) has Lebesgue \(m\)- measure zero. The paper contains two sections: (1) singular mappings of finite-dimensional spaces; (2) critical images in Banach spaces. It is a nice continuation of the author's previous paper [Proc. Am. Math. Soc. 114, No. 3, 699-705 (1992; Zbl 0749.58011)].
scientific article; zbMATH DE number 179203
scientific article