An elementary example of Sard's Theorem sharpness

Abstract

In this note we define a $C^1$ function $F:[0,M{]}^2\to [0,2]$ that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differentiability required in Sard's Theorem cannot be improved

4 pages note-