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MR1143222 (93k:28007) 28A80 (26A30)
Darst, Richard The Hausdorff dimension of the nondifferentiability set of the Cantor function is $[{\rm ln}(2)/{\rm ln}(3)]\sp 2$. Proc. Amer. Math. Soc. 119 (1993), no. 1, 105–108.
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