You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
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
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
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