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.

Click here for an online copy of this paper from JSTOR.

Click here for a PostScript copy (150K) of this paper.

Back to my list of recent papers.

Back to my home page.

Last updated: June 23, 1998