A dyadic endomorphism which is Bernoulli but not standard (Q696297)

The authors consider a simple example -- a one-sided Bernoulli shift with two states \(X=\{0,1\}^N\) and the \((1/2,1/2)\) product measure. This endomorphism has two basic properties: it generates a decreasing sequence of \(\sigma\)-algebras and has an invertible extension. The authors find another measure preserving endomorphism whose invertible extension is isomorphic to that of the Bernoulli shift but which generates a different, nonisomorphic sequence of \(\sigma\)-algebras.