Dimension of Besicovitch–Eggleston sets in countable symbolic space

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 dime...

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Veröffentlicht in:	Nonlinearity 2010-05, Vol.23 (5), p.1185-1197
Hauptverfasser:	Fan, Aihua, Liao, Lingmin, Ma, Jihua, Wang, Baowei
Format:	Artikel
Sprache:	eng
Schlagworte:	Digits Exact sciences and technology Global analysis, analysis on manifolds Lower bounds Mathematical methods in physics Mathematics Nonlinearity Other topics in mathematical methods in physics Physics Real numbers Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Zusammenfassung:	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.
ISSN:	0951-7715 1361-6544
DOI:	10.1088/0951-7715/23/5/009