Geodesic
On the Pyatetskii-Shapiro Criterion of Normality
Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 577-589

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In this paper, the Postnikov–Pyatetskii-Shapiro criterion of normality is given a more modern form. We obtain its unimprovable analogs for finite Markov chains, continued fractions, and generalized Bernoulli shifts. 
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N. G. Moshchevitin; I. D. Shkredov. On the Pyatetskii-Shapiro Criterion of Normality. Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 577-589. http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a9/