A simple proof of the Morse-Sard theorem in Sobolev spaces

Abstract

In this paper we give a new simple proof of a result of Luigi De Pascale, which states that the Morse-Sard Theorem holds under the hypothesis of Sobolev regularity. Moreover, as our proof is independent of the Morse Sard Theorem with Ck regularity, our result implies the classical Morse-Sard Theorem. The Morse-Sard Theorem is concerned with the size of the image of the critical values of a differentiate function. To recall it and to state our result, we need some definitions.