Occupation times of sets of infinite measure for ergodic transformations

Abstract

Assume that T is a conservative ergodic measure preserving transformation of the infinite measure space (X,A,µ). We study the asymptotic behaviour of occupation times of certain subsets of infinite measure. Specifically, we prove a Darling-Kac type distributional limit theorem for occupation times of barely infinite components which are separated from the rest of the space by a set of finite measure with c.f.-mixing return process. In the same setup we show that the ratios of occupation times of two components separated in this way diverge almost everywhere. These