Ergodic Theory and Dynamical Systems

Table of Contents - 01 March 1992 - Volume 12, Issue 01  

Research Article

Random sets for the pointwise ergodic theorem

Yenkun Huanga1

a1 Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan, Republic of China

Abstract

We generalize a result of Bourgain and devise more general criteria which guarantee that the corresponding random set in Z+ almost surely satisfies a pointwise ergodic theorem on Lp for p > 1. Several large classes of examples are constructed. We also show that under a simple condition the corresponding random set in Z+ almost surely satisfies a pointwise ergodic theorem not only on Lp for p > 1 but also on L1. On the other hand, we establish a criterion to conclude that a certain class of random sets have Banach density zero. In particular, all of the examples mentioned have Banach density zero.

(Received September 20 1990)

(Revised March 12 1991)