The Denjoy-Young-Saks Theorem in Higher Dimensions: A Survey

Abstract

The classical theorem of Denjoy, Young and Saks gives a relation between Dini derivatives of a real variable function that holds almost everywhere. We present what is known in the one and two variable case with an emphasis on the latter. Relations that hold a.e. in both the measure and category sense are considered. Classical and approximate derivatives are both discussed.