Denjoy-Young-Saksʼs Theorem for Approximate Derivatives Revisited

Abstract

We note that the restriction of any measurable mapping $fR\to {\text{R}}^n$ to the set of points at which it possesses a finite approximate derived number maps Lebesgue null sets to sets of zero linear measure. As a corollary we deduce an optimal version of Denjoy-Young-Saks's theorem for approximate derivatives valid up to exceptional sets of zero linear measure in the graph.