One class of singular complex-valued random variables of the Jessen-Wintner type
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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.
KeywordsProbability Measure Fractal Property Discrete Distribution Sierpinski Carpet Additive Probability Measure
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