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

The prevalence of continuous nowhere differentiable functions


Author: Brian R. Hunt
Journal: Proc. Amer. Math. Soc. 122 (1994), 711-717
MSC: Primary 26A27; Secondary 26A16, 28C20, 60B11
MathSciNet review: 1260170
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Abstract: In the space of continuous functions of a real variable, the set of nowhere differentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a measure theoretic sense (which is different from Wiener measure), "almost every" continuous function is nowhere differentiable. Similar results concerning other types of regularity, such as Hölder continuity, are discussed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1260170-X
PII: S 0002-9939(1994)1260170-X
Article copyright: © Copyright 1994 American Mathematical Society