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

摘要

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.