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The Prevalence of Continuous Nowhere Differentiable Functions

Brian R. Hunt
Proceedings of the American Mathematical Society
Vol. 122, No. 3 (Nov., 1994), pp. 711-717
DOI: 10.2307/2160745
Stable URL: http://www.jstor.org/stable/2160745
Page Count: 7
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The Prevalence of Continuous Nowhere Differentiable Functions
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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 Holder continuity, are discussed.

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