β-automorphisms are Bernoulli shifts
✍ Scribed by M. Smorodinsky
- Publisher
- Akadmiai Kiad
- Year
- 1973
- Tongue
- English
- Weight
- 253 KB
- Volume
- 24
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The purpose of this paper is to prove the following result. THEOREM 1. If u' is a Bernoulli shift with Jinite entropy on a probability space (Y', 9', v'), and E > 0 then there exists a probability space (X, F, CL) containing (Y', 9, v') (in the sense that Y' E 9, 9' = S Iy, = {FE 9 : F C Y'}, V' = ,
Bernoulli shift is an invertible measure preserving transformation on the unit interval with Lebesgue measure that admits an independent generator, i.e., there exists a partition of the unit interval into a finite or countable number of disjoint sets of positive measure such that distinct iterates u
We define a generalized Bernoulli shift as follows: Let Y be a measure space of total measure 1 consisting of a part (possibly empty) that is isomorphic to an interval and a part (possibly empty) consisting of a finite or countable number of atoms. Let X = n\_", Yi be the product of a countable numb