Ukrainian Mathematical Journal

, Volume 49, Issue 12, pp 1862–1871 | Cite as

One class of singular complex-valued random variables of the Jessen-Wintner type

  • O. V. Shkol’nyi
  • M. V. Prats’ovytyi


We study the structure of the distribution of a complex-valued random variable ξ = Σa k ξ k , where ξ k are independent complex-valued random variables with discrete distribution and a k are terms of an absolutely convergent series. We establish a criterion of discreteness and sufficient conditions for singularity of the distribution of ξ and investigate the fractal properties of the spectrum.


Probability Measure Fractal Property Discrete Distribution Sierpinski Carpet Additive Probability Measure 
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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • O. V. Shkol’nyi
  • M. V. Prats’ovytyi

There are no affiliations available

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