Stationary (in Strict Sense) Random Sequences and Ergodic Theory

Abstract

Let T be any measure preserving transformation acting on the sample space Ω and let ξ = ξ(ω), ω ∈ Ω, be any random variable, chosen so that the expected value Eξ(ω) exists. Prove that Eξ(ω) =Eξ(Tω).