*Published Paper*

**Inserted:** 5 dec 2000

**Last Updated:** 6 mar 2007

**Journal:** Real Anal. Exchange

**Volume:** 26 (2000/01)

**Number:** 1

**Pages:** 485-488

**Year:** 2000

**Abstract:**

Let f be a vector-valued, measurable map on the line. and let D be the set of points at which it possesses a finite approximate derived number. We note that the restriction of f to the set D 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.

**Keywords:**
Denjoy-Young-Saks theorem, approximate Dini derivatives, Lusin (N) property

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