Projective limits of measure preserving transformations on probability spaces

Abstract

Using the method of algebraic models, it is proved first that the projective limit T of a projective system of measure preserving transformations T α exists and is unique, modulo conjugacy, and then that if T α are ergodic with discrete spectrum, or totally ergodic (all iterates ergodic) with quasi-discrete spectrum, then T has the same property. An open problem is whether T has discrete model if all T α have discrete models.