Dimension of Besicovitch–Eggleston sets in countable symbolic space

Abstract

This paper is mainly concerned with Hausdorff dimensions of Besicovitch–Eggleston subsets in countable symbolic space. A notable point is that the dimension values possess a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dimension formulae for sets of real numbers with prescribed digit frequencies in their Lüroth expansions.