2019
Том 71
№ 8

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

O. V. Shkol’nyi

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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).

English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 12, pp 1956-1962.

Citation Example: O. V. Shkol’nyi Random variables determined by the distributions of their digits in a numeration system with complex base // Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1715–1720.

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