The Hausdorff dimension of the nondifferentiability set of the Cantor function is [𝑙𝑛(2)/𝑙𝑛(3)]²

Darst, Richard

doi:10.1090/S0002-9939-1993-1143222-3

The Hausdorff dimension of the nondifferentiability set of the Cantor function is $[\textrm {ln}(2)/\textrm {ln}(3)]^ 2$
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Proc. Amer. Math. Soc. 119 (1993), 105-108 Request permission

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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