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 systembecomes almost surely normal over all bases multiplicatively independent of r.
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Original Russian Text © L. N. Pushkin, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 6, pp. 884–891.
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Pushkin, L.N. On the behavior of the spectrum of the limit frequencies of digits under perturbations of a real number. Math Notes 86, 824–830 (2009). https://doi.org/10.1134/S0001434609110248
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DOI: https://doi.org/10.1134/S0001434609110248