We note that the restriction of any measurable mapping $f: R \to R^n$ 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.
Denjoy-Young-Saks theorem for approximate derivatives revisited
ALBERTI, GIOVANNI;
2001-01-01
Abstract
We note that the restriction of any measurable mapping $f: R \to R^n$ 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.File in questo prodotto:
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