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Matematicheskie Zametki, 2009, Volume 86, Issue 6, Pages 884–891
DOI: https://doi.org/10.4213/mzm4150 (Mi mzm4150) 		 
On the Behavior of the Spectrum of the Limit Frequencies of Digits under Perturbations of a Real Number

L. N. Pushkin

Kazan State University
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DOI: https://doi.org/10.4213/mzm4150
Abstract: It is shown that, under the action of random digitwise decaying perturbations not changing the spectrum of the limit frequencies of $r$-adic digits, an arbitrary real number written in the $r$-adic number system becomes almost surely normal over all bases multiplicatively independent of $r$.
Keywords: $r$-adic number system, normal number, digitwise perturbations of a number, spectrum of limit frequencies of digits, Lebesgue measure.
Received: 09.03.2005
English version:
Mathematical Notes, 2009, Volume 86, Issue 6, Pages 824–830
DOI: https://doi.org/10.1134/S0001434609110248
Bibliographic databases:
UDC: 511.37+519.21
Language: Russian
Citation: L. N. Pushkin, “On the Behavior of the Spectrum of the Limit Frequencies of Digits under Perturbations of a Real Number”, Mat. Zametki, 86:6 (2009), 884–891; Math. Notes, 86:6 (2009), 824–830
Citation in format AMSBIB
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