Ergodic Theory and Dynamical Systems

Research Article

Necessary and sufficient conditions for a maximal ergodic theorem along subsequences

Roger L. Jonesa1

a1 Department of Mathematics, DePaul University, Chicago, IL 60614, USA

Abstract

Let T be an ergodic measure preserving point transformation from a probability space X onto itself. Assume that is an increasing sequence of subsets of the positive integers. Conditions are given which are sufficient for the ergodic maximal function associated with these subsets to be weak type (p, p). These conditions are shown to be both necessary and sufficient for a larger two-sided maximal function. The conditions are in the form of covering lemmas for the integers.

(Received November 05 1985)