Inserted: 5 dec 2000
Last Updated: 6 mar 2007
Journal: Real Anal. Exchange
Volume: 26 (2000/01)
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