Open Access
2000/2001 On Dini and Approximate Dini Derivates of Typical Continuous Functions
L. Zajíček, D. Preiss
Real Anal. Exchange 26(1): 401-412 (2000/2001).


In the thirties, Banach, Mazurkiewicz and Jarn\'{\i}k found relations connecting Dini derivates of a typical continuous function on $[0,1]$ at all points of $(0,1)$. We prove, answering a question of K. M. Garg, that there are no further relations of this sort. An analogous result is proved also for approximate Dini derivates. The aim of this note is to present relatively simple proofs of these results. An article containing an improvement of these results in several directions (with a considerably more complicated proof) is in preparation.


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L. Zajíček. D. Preiss. "On Dini and Approximate Dini Derivates of Typical Continuous Functions." Real Anal. Exchange 26 (1) 401 - 412, 2000/2001.


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

zbMATH: 1009.26010
MathSciNet: MR1825518

Primary: 26A24

Keywords: Dini approximate derivate , Dini derivate , typical continuous function

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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