Uniform endomorphisms which are isomorphic to a Bernoulli shift (Q1852702)

Ornstein and Weiss introduced the notion of very weak Bernoulli as a criterion for proving that certain automorphisms are isomorphic to Bernoulli shifts. The situation for endomorphisms is more complicated. In this paper the authors introduce a concept called tree very weak Bernoulli which is useful for showing that certain endomorphisms are isomorphic to one-sided Bernoulli shifts. Using this criteria, they are able to show that a class of two-to-one endomorphisms, known as the \([T,\text{Id}]\) examples, are conjugate to the standard two-to-one endomorphism.