Published Paper
(2000)
Authors:
Giovanni Alberti - Marianna Csörnyei - Miklós Laczkovich - David Preiss
Journal: Real Anal. Exchange [MathSciNet]
Volume: 26 (2000/01)
Number: 1
Pages: 485-488
Keywords:
Denjoy-Young-Saks theorem, approximate Dini derivatives, Lusin (N) property
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.
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[BibTeX Entry]
Available Files:
derivatives.pdf
abstract.tex (abstract.ps, abstract.pdf)
