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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The Hausdorff dimension of the nondifferentiability set of the Cantor function is $ [{\rm ln}(2)/{\rm ln}(3)]\sp 2$


Author: Richard Darst
Journal: Proc. Amer. Math. Soc. 119 (1993), 105-108
MSC: Primary 28A80; Secondary 26A30
MathSciNet review: 1143222
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Abstract: The main purpose of this note is to verify that the Hausdorff dimension of the set of points $ {N^{\ast}}$ at which the Cantor function is not differentiable is $ {[\ln (2)/\ln (3)]^2}$. It is also shown that the image of $ {N^{\ast}}$ under the Cantor function has Hausdorff dimension $ \ln (2)/\ln (3)$. Similar results follow for a standard class of Cantor sets of positive measure and their corresponding Cantor functions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1143222-3
PII: S 0002-9939(1993)1143222-3
Article copyright: © Copyright 1993 American Mathematical Society