# zbMATH — the first resource for mathematics

$$\beta$$-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.
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.