Dimension of Besicovitch-Eggleston sets in countable symbolic space

作者:Fan Aihua*; Liao Lingmin; Ma Jihua; Wang Baowei
来源:Nonlinearity, 2010, 23(5): 1185-1197.
DOI:10.1088/0951-7715/23/5/009

摘要

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 Luroth expansions.