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Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions

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Ukrainian Mathematical Journal Aims and scope

Abstract

We study the fractal properties (we find the Hausdorff-Bezikovich dimension and Hausdorff measure) of the spectrum of a random variable with independentn-adic (n≥2,n ∃N digits, the infinite set of which is fixed. We prove that the set of numbers of the segment [0, 1] that have no frequency of at least onen-adic digit is superfractal.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. V. Pratsevityi

  2. Ukrainian Pedagogical University, Kiev

    G. M. Torbin

Authors
  1. N. V. Pratsevityi
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  2. G. M. Torbin
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Additional information

Translated from Ukrainskii Matematicheskii Zhumal, Vol. 47, No. 7, pp. 971–975, July, 1995.

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Pratsevityi, N.V., Torbin, G.M. Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions. Ukr Math J 47, 1113–1118 (1995). https://doi.org/10.1007/BF01084907

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  • DOI: https://doi.org/10.1007/BF01084907

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