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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160745
Page Count: 7
You can always find the topics here!Topics: Mathematical functions, Differentiable functions, Differential topology, Integers, Continuous functions, Topological theorems, Lebesgue measures, Borel sets, Topological regularity
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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.
Proceedings of the American Mathematical Society © 1994 American Mathematical Society