Two Bernoulli shifts with infinite entropy are isomorphic

✍ Scribed by Donald Ornstein

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 456 KB
• Volume: 5
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(70)90008-3

✦ Synopsis

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 number of copies, Yi , of Y with the product measure.

Let T be the shift on X (each point of X is a sequence {yi} of points in Y and T{y,} = (yi'> and yi' = yi+r).