Isomorphisms of certain correlated probability spaces and of discrete memoryless correlated sources (Q1077078)

In Z. Wahrscheinlichkeitstheor. Verw. Geb. 63, 51-58 (1983; Zbl 0488.60049), we defined a sufficient set of invariants for the isomorphy of discrete memoryless correlated sources with maximal correlation \(<1\). Using the structure of isomorphisms of certain correlated probability spaces, we give here a sufficient set of invariants also for the case of maximal correlation equal to 1. We show, in particular, that two discrete memoryless stationary correlated sources with maximal correlation 1 may be isomorphic in a nontrivial way.