aequationes mathematicae

, Volume 72, Issue 1–2, pp 10–26 | Cite as

A generalization of a result by W. Li and F. Dekking on the Hausdorff dimension of subsets of self-similar sets with prescribed group frequency of their codings

Research paper


Let K be a self-similar set in \({\mathbb{R}}^{d}\) satisfying the Open Set Condition. Recently Li and Dekking computed the Hausdorff dimension of the set of points in K with prescribed frequencies of groups of digits in their codings (as opposed to the Hausdorff dimension the set of points with prescribed frequencies of digits in their codings). In this paper we show that the methods and techniques from multifractal analysis of divergence points developed in [Ol1, Ol2, OW1, OW2] can be applied to give a simple proof of a substantial generalization of this result.

Mathematics Subject Classification (2000).



Hausdorff dimension normal numbers non-normal numbers frequencies of families of digits divergence points 


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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of St. AndrewsSt. Andrews, FifeScotland

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