On preponderant differentiability of typical continuous functions
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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 $(0,1)$.References
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Additional Information
- L. Zajíček
- Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic
- Email: Zajicek@karlin.mff.cuni.cz
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 789-798
- MSC (1991): Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9939-96-03057-2
- MathSciNet review: 1291796