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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On preponderant differentiability
of typical continuous functions


Author: L. Zajícek
Journal: Proc. Amer. Math. Soc. 124 (1996), 789-798
MSC (1991): Primary 26A24
MathSciNet review: 1291796
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Abstract: In the literature, several definitions of a preponderant derivative exist. An old result of Jarník implies that a typical continuous function on $ \ [0,1] \ $ has a (strong) preponderant derivative at no point. We show that a typical continuous function on $ \ [0,1] \ $ has an infinite (weak) preponderant derivative at each point from a $c$-dense subset of $ \ (0,1) $.


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Additional Information

L. Zajícek
Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic
Email: Zajicek@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03057-2
PII: S 0002-9939(96)03057-2
Keywords: Preponderant derivative, typical continuous function, Banach-Mazur game
Received by editor(s): March 15, 1994
Received by editor(s) in revised form: August 23, 1994
Additional Notes: Supported by Research Grants GAUK 363 and GAČR 0474.
Communicated by: C. D. Sogge
Article copyright: © Copyright 1996 American Mathematical Society