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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On preponderant differentiability of typical continuous functions
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by L. Zajíček PDF
Proc. Amer. Math. Soc. 124 (1996), 789-798 Request permission

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. 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