On the Piatetskii-Shapiro criterion of normality. (English. Russian original) Zbl 1173.37302

Moshchevitin, N. G.; Shkredov, I. D.

Math. Notes 73, No. 4, 539-550 (2003); translation from Mat. Zametki 73, No. 4, 577-589 (2003).

Summary: 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.

MSC:

37A30	Ergodic theorems, spectral theory, Markov operators
11K50	Metric theory of continued fractions
28D05	Measure-preserving transformations
37A45	Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

criterion of normality; finite Markov chain; dynamical system; Hausdorff measure; continued fraction; Bernoulli shift; central limit theorem; large deviations