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On preponderant differentiability of typical continuous functions

Author(s): L. Zajícek
Journal: Proc. Amer. Math. Soc. 124 (1996), 789-798.
MSC (1991): Primary 26A24
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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: 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 GACR 0474.
Communicated by: C. D. Sogge
Copyright of article: Copyright 1996, American Mathematical Society

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