Ergodic properties of sets defined by the frequencies of digits

dc.contributor.author	Pushkin L.
dc.date.accessioned	2018-09-17T21:51:18Z
dc.date.available	2018-09-17T21:51:18Z
dc.date.issued	1996
dc.identifier.issn	0040-585X
dc.identifier.uri	https://dspace.kpfu.ru/xmlui/handle/net/135521
dc.description.abstract	Let ξ1,ξ2,. . . be a random sequence of r-ary digits, r ∈ N\{1}, connected into an ergodic Markov chain. Let β > 1 be an algebraic number such that the ratio log β/log r is irrational. Then with probability one, the number ξ= ∑∞ j=1 ξjr-j is normal with respect to the radix β. The proof is based on the Gelfand-Baker estimate for the absolute value of a linear form in the logarithms of algebraic numbers.
dc.relation.ispartofseries	Theory of Probability and its Applications
dc.subject	Cassels-Schmidt theorem
dc.subject	Finite Markov chains
dc.subject	Gelfand-Baker's theory
dc.subject	Normal numbers
dc.subject	The estimates for the characteristic functions of singular distributions
dc.title	Ergodic properties of sets defined by the frequencies of digits
dc.type	Article
dc.relation.ispartofseries-issue	3
dc.relation.ispartofseries-volume	41
dc.collection	Публикации сотрудников КФУ
dc.relation.startpage	593
dc.source.id	SCOPUS0040585X-1996-41-3-SID0030336885

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Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.