On the Piatetskii-Shapiro criterion of normality

DOI10.1023/A:1023263305857zbMath1173.37302OpenAlexW67663107MaRDI QIDQ1886133

Ilya D. Shkredov, Nikolay G. Moshchevitin

Publication date: 15 November 2004

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1023263305857

zbMATH Keywords

dynamical systemcentral limit theoremlarge deviationsHausdorff measureBernoulli shiftcontinued fractionfinite Markov chaincriterion of normality

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Ergodic theorems, spectral theory, Markov operators (37A30) Metric theory of continued fractions (11K50)

Related Items (9)

Construction of \(\mu \)-normal sequences ⋮ Insertion in constructed normal numbers ⋮ Non-trivial matrix actions preserve normality for continued fractions ⋮ Hotspot lemmas for noncompact spaces ⋮ Generic point equivalence and Pisot numbers ⋮ On the Pyatetskii-Shapiro normality criterion for continued fractions ⋮ Preservation of normality by non-oblivious group selection ⋮ A Hot Spot Proof of the Generalized Wall Theorem ⋮ An analogue of Pillai's theorem for continued fraction normality and an application to subsequences

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