Some remarks about the Morse-Sard theorem and approximate differentiability (Q2303545)

The authors make several remarks on the relationship between approximate differentiability of higher order and the Morse-Sard property. For instance, they show that if a function \(f:{\mathbb R}^n \rightarrow {\mathbb R}^m\) (with \(n, m\) positive integers, \(n \geq m\)) is locally Lipschitz and approximately differentiable of order \(i\) almost everywhere with respect to the \((i+m-2)\)-Hausdorff measure, for every \(i = 2,\dots, n-m + 1\), then \(f\) has the Morse-Sard property (that is to say, the image of the critical set of \(f\) is null with respect to the Lebesgue measure in \({\mathbb R}^m\)).