Flows Associated with Ergodic Non-Singular Transformation Groups

Abstract

In this paper we shall give a nice invariant for the weak equivalence of ergodic non-singular transformation groups. It is a one-parameter ergodic non-singular flow associated with an ergodic non-singular transformation group. Since in 1960 an example of an ergodic non-singular transformation without <r-finite invariant measures was given in Ergodic theory Among these works, Krieger's weak equivalence theory is fundamental in the classification problem of ergodic nonsingular transformation groups without er-finite invariant measures. This classification is closely connected with the classification of type III factors in the theory of von Neumann algebras ([15]).