The prevalence of continuous nowhere differentiable functions

Hunt, Brian R.

doi:10.1090/S0002-9939-1994-1260170-X

The prevalence of continuous nowhere differentiable functions
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by Brian R. Hunt

Proc. Amer. Math. Soc. 122 (1994), 711-717

DOI: https://doi.org/10.1090/S0002-9939-1994-1260170-X

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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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