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Ukrainian Mathematical Journal

, Volume 50, Issue 12, pp 1956–1962 | Cite as

Random variables determined by the distributions of their digits in a numeration system with complex base

  • O. V. Shkol’nyi
Brief Communications
  • 16 Downloads

Abstract

We study the distributions of complex-valued random variables determined by the distributions of their digits in a numeration system with complex base. We establish sufficient conditions for the singularity of such random variables, in particular, in the cases where their spectrum has Lebesgue measure zero (C-type singular distribution) or is a rectangle (S-type singular distribution).

Keywords

Complex Base Ukrainian Academy Numeration System Lebesgue Measure Zero Singular Distribution 
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References

  1. 1.
    O. V. Shkol’nyi, “On one class of singular complex-valued random variables of the Jessen-Wintner type,” Ukr. Mat. Zh., 49, No. 12. 1653–1660 (1997).CrossRefGoogle Scholar
  2. 2.
    A. F. Turbin and N. V. Pratsevityi, Fractal Sets, Functions, and Distributions[in Russian], Naukova Dumka, Kiev (1992).Google Scholar
  3. 3.
    N. V. Pratsevityi, “Classification of singular distributions depending on the spectrum properties,” in: Random Evolutions: Theoretical and Applied Problems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 77–83.Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • O. V. Shkol’nyi
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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