Stability of m-equivalence to the weak Pinsker property

Adam Fieldsteel, Daniel J. Rudolph
1990 Ergodic Theory and Dynamical Systems  
Let W9> denote the class of transformations with the weak Pinsker property, and let [W0>] m denote the class of transformations m-equivalent to some member of W9, where m is an entropy-preserving size. We show that if T is a factor of an element of [T0>] m , then Te[W@] m , and if T is an m-limit of elements of [W9>] m , then Te{°W9] m . In this paper we apply the theory of restricted orbit equivalences of ergodic transformations, as developed in the recent memoir of Rudolph [2] , to the study
more » ... [2] , to the study of the weak Pinsker property. We begin with a brief summary of some of the basic ideas in Rudolph's work. Let T be an ergodic transformation. (Throughout this paper, all transformations are assumed to be, or may be shown to be ergodic measure-preserving transformations of a Lebesgue probability space.) We define an integer-valued function a on the orbit relation determined by T by a(w, «') = n if T"(a>) = «', and refer to a as an ordering. We may indicate the relation between T and a by writing T as T a . By an orbit equivalence we mean a pair of transformations T and T' on the same space with the same orbits, hence giving (and being given by) two orderings. If a and a' are two such orderings, the orbit equivalence they represent, denoted (a, a')
doi:10.1017/s0143385700005423 fatcat:zjmcuyrahvbs5llvyfjabqphya