Random variables determined by the distributions of their digits in a numeration system with complex base
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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).
KeywordsComplex Base Ukrainian Academy Numeration System Lebesgue Measure Zero Singular Distribution
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