Return times for nonsingular measurable transformations

Abstract

Let σ be a nonsingular antiperiodic automorphism of a Lebesgue probability space . Let π = ( π 1, π 2, …, π k , …) be a probability vector with the property that the k's for which π k > 0 is a relatively prime set of integers and ∑ i = 1 ∞ iπ i < ∞. Then there is a measurable set B of positive measure such that the relative distribution of return times under σ to B is the given distribution.