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Hausdorff dimensions of sets related to Lüroth expansion

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Abstract

We study two classes of sets of real numbers related to Lüroth expansions and obtain their Hausdorff dimensions. One is determined by prescribed group frequencies of digits in their Lüroth expansions. It is proved that the Hausdorff dimension of such a set is equal to the supremum of the Hausdorff dimensions for sets of real numbers with prescribed digit frequencies in their Lüroth expansion. The other is determined by randomly selecting the digits in their Lüroth expansion from a finite number of given digit sets.

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Authors and Affiliations

  1. School of Mathematics and Statistics, HuBei University of Science and Technology, Xianning, 437100, P. R. China

    Y. Gui

  2. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, P. R. China

    W. Li

Authors
  1. Y. Gui
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  2. W. Li
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Correspondence to W. Li.

Additional information

Supported by the excellent mid-youth innovative team project of Hubei Provincial Education Department #T201009.

Partially supported by the National Natural Science Foundation of China No. 11271137, 11571144, 11671147 and Science and Technology Commission of Shanghai Municipality (STCSM), grant No. 13dz2260400.

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Gui, Y., Li, W. Hausdorff dimensions of sets related to Lüroth expansion. Acta Math. Hungar. 150, 286–302 (2016). https://doi.org/10.1007/s10474-016-0661-7

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  • DOI: https://doi.org/10.1007/s10474-016-0661-7

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