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Dimensions of weighted Besicovitch sets

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Abstract

We consider weighted Besicovitch sets which are defined in terms of the weighted frequency of digit 1 in the dyadic expansion of real numbers. Explicit formulas for their Hausdorff dimensions are given.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan, 430070, P. R. China

    Yu Qiong Xie

  2. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China

    Zhi Xiong Wen

  3. School of Science, Wuhan University of Science and Technology, Wuhan, 430081, P. R. China

    Min Yu

Authors
  1. Yu Qiong Xie
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  2. Zhi Xiong Wen
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  3. Min Yu
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Corresponding author

Correspondence to Yu Qiong Xie.

Additional information

Supported by the Special Fund for Major State Basic Research Projects (Grant No. 60472041)

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Xie, Y.Q., Wen, Z.X. & Yu, M. Dimensions of weighted Besicovitch sets. Acta. Math. Sin.-English Ser. 26, 711–716 (2010). https://doi.org/10.1007/s10114-010-7499-7

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  • DOI: https://doi.org/10.1007/s10114-010-7499-7

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