The Prevalence of Continuous Nowhere Differentiable Functions
- 1 November 1994
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 122 (3) , 711-717
- https://doi.org/10.2307/2160745
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.Keywords
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