Structure of level sets and Sard-type properties of Lipschitz maps

We consider certain properties of maps of class $C^2$ from $R^d$ to $R^{d1}$ that are strictly related to Sard’s theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give counterexamples showing that, in term of regularity, our results are optimal