Geodesic
On the Behavior of the Spectrum of the Limit Frequencies of Digits under Perturbations of a Real Number
Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 884-891

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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
Mots-clés : Lebesgue measure. 
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     author = {L. N. Pushkin},
     title = {On the {Behavior} of the {Spectrum} of the {Limit} {Frequencies} of {Digits} under {Perturbations} of a {Real} {Number}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {884--891},
     publisher = {mathdoc},
     volume = {86},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a6/}
}
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L. N. Pushkin. On the Behavior of the Spectrum of the Limit Frequencies of Digits under Perturbations of a Real Number. Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 884-891. http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a6/