Some Aspects of Ornstein's Theory of Isomorphism Problems in Ergodic Theory

Abstract

In a series of recent papers E^IhL^H, D. Ornstein and Friedman carried out fundamentally important investigations about metrical isomorphism in ergodic theory. Motivated by the papers, the authors of [JQ and the present paper were engaged in allied isomorphism problems, especially those when generators are not finite and entropies are infinite. Using Ornstein's ideas, the authors of the two papers independently have arrived at similar results. However, the approaches and techniques in the both papers are different. In the present paper, basically we only assume several fundamental results from F7]. In several respects we can simplify and refine the techniques of Q7], thus not using the method in Q5], we prove in § 4 a generalized version of the main theorem of £5], The basic probability measure space (£, m, . A ^P-set is that which is represented as a