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Fractal dimensions of some sets in [0, 1)

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Approximation Theory and its Applications

Abstract

A kind of fractal sets, non-regular sets with 0-Lebesgue measure, is introduced by considering binary expansion of real numbers in [0,1). Their fractal dimensions are also studied in this paper.

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Reference

  1. Eggleston, H. G., The Fractional Dimension of a Set Defined by Decimal Properties, Q. J. Math. Oxford, 1949, 20: 31–46.

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  2. Falconer, K. J., Fractal Geometry: Mathematical Foundation and Applications, Chichester: John Wiley & Sons, 1990.

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  3. Mauldin, R. D. and Urbanski M., Dimensions and Measures in Infinite Iterated Function Systems, Proc. London. Math. Soc. Vol. 73(1996), 105–154.

    Article  MATH  MathSciNet  Google Scholar 

  4. Gould, H. W., Combinatorial Identities, Morgantown Printing and Binding Co.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Nanjing, PRC

    Xu Yong, Sun Qingjie & Su Weiyi

Authors
  1. Xu Yong
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  2. Sun Qingjie
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  3. Su Weiyi
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Additional information

In Memory of Professor M. T. Cheng

Project supported by the “Padeng” Program of China.

Now working as a postdoctor in the network center of South China University of Technoligy in Guang Zhou

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Yong, X., Qingjie, S. & Weiyi, S. Fractal dimensions of some sets in [0, 1). Approx. Theory & its Appl. 15, 23–28 (1999). https://doi.org/10.1007/BF02848667

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  • DOI: https://doi.org/10.1007/BF02848667

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