Open Access
2000/2001 Denjoy-Young-Saksʼs Theorem for Approximate Derivatives Revisited
Giovanni Alberti, Marianna Csörnyei, Miklós Laczkovich, David Preiss
Real Anal. Exchange 26(1): 485-488 (2000/2001).


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.


Download Citation

Giovanni Alberti. Marianna Csörnyei. Miklós Laczkovich. David Preiss. "Denjoy-Young-Saksʼs Theorem for Approximate Derivatives Revisited." Real Anal. Exchange 26 (1) 485 - 488, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1009.26009
MathSciNet: MR1825530

Primary: 26A24 , 28A75

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

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
Back to Top