Calculus of Variations and Geometric Measure Theory

G. Alberti - M. Csörnyei - M. Laczkovich - D. Preiss

Denjoy-Young-Saks theorem for approximate derivatives revisited

created on 05 Dec 2000
modified by alberti on 06 Mar 2007


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


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