Distribution of frequencies of digits via multifractal analysis
Unifying classical results of Borel, Besicovitch, Eggleston, and Billingsley in several directions, the authors study the Hausdorff dimension of a large class of sets in the real line defined in terms of the distribution of frequencies of digits for the representation in some integer base. The methods are based on recent results concerning the multifractal analysis of dynamical systems and often lead to explicit expressions for the Hausdorff dimension.
scientific article; zbMATH DE number 1891450