ON YOUNG TOWERS ASSOCIATED WITH INFINITE MEASURE PRESERVING TRANSFORMATIONS

Abstract

For a σ-finite measure preserving dynamical system (X, μ, T), we formulate necessary and sufficient conditions for a Young tower (Δ, ν, F) to be a (measure theoretic) extension of the original system. Because F is pointwise dual ergodic by construction, one immediate consequence of these conditions is that the Darling–Kac theorem carries over from F to T. One advantage of the Darling–Kac theorem in terms of Young towers is that sufficient conditions can be read off from the tail behavior and we illustrate this with relevant examples. Furthermore, any two Young towers with a common factor T, have return time distributions with tails of the same order.