Endomorphisms of a Lebesgue space III

A new invariant is introduced for regular isomorphisms, which are isomorphisms by codes that anticipate a finite amount of the future. With the help of this invariant it is shown that the Bernoulli automorphism (p, q) is not regularly isomorphic to the Markov automorphism ( _pq ^qp ),p ≠q, and that neither of these is regularly isomorphic to the Markov automorphism ( _qp ^pq ).