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\(\beta\)-automorphisms are Bernoulli shifts. (English) Zbl 0268.28007

MSC:
28D05 Measure-preserving transformations
11K06 General theory of distribution modulo \(1\)
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
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[1] P. Billingsley,Ergodic theory and information, Wiley, 1965. · Zbl 0141.16702
[2] N. A. Friedman–D. S. Ornstein, On isomorphism of weak Bernoulli transformations,Advances in Math.,5 [3] (1970), pp. 365–394. · Zbl 0203.05801 · doi:10.1016/0001-8708(70)90010-1
[3] W. Parry, On the \(\beta\)-expansion of real numbers,Acta. Math. Acad. Sci. Hung.,11 (1960), pp. 401–416. · Zbl 0099.28103 · doi:10.1007/BF02020954
[4] A. Rényi, Representations for real numbers and their ergodic properties,Acta. Math. Acad. Sci. Hung.,8 (1957), pp. 472–493.
[5] V. A. Rokhlin, Exact endomorphisms of a Lebesgue space,Izv. Akad. Nauk SSSR, Ser. Mat.,24 (1960);English AMS Translation, Series2, Vol.39 (1969), pp. 1–36.
[6] M. S. Waterman, Some ergodic properties of multidimensionalF-expansions,Z. Wahrscheinlichkeitsrechnung,16 (1970), pp. 77–103. · Zbl 0199.37102 · doi:10.1007/BF00535691
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