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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 Luroth expansions.
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Submitted on : Tuesday, May 1, 2012 - 7:34:22 PM
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Aihua Fan, Lingmin Liao, Jihua Ma, Baowei Wang. Dimension of Besicovitch-Eggleston sets in countable symbolic space. Nonlinearity, IOP Publishing, 2010, 23 (5), pp.1185--1197. ⟨10.1088/0951-7715/23/5/009⟩. ⟨hal-00693023⟩



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