The Prevalence of Continuous Nowhere Differentiable Functions

Brian R. Hunt

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

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, ``almost every'' continuous function is nowhere differentiable. Similar results concerning other types of regularity, such as H\"older continuity, are discussed.

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