THE POINTWISE ERGODIC THEOREM FOR AMENABLE GROUPS. 473 among other
things, that the appropriate ergodic averages always converge in norm to a G-invariant …

In this paper we prove the pointwise ergodic theorem for general locally compact amenable
groups along Følner sequences that obey some restrictions. These restrictions are mild …

In this paper we describe proofs of the pointwise ergodic theorem and Shannon-McMillan-
Breiman theorem for discrete amenable groups, along Følner sequences that obey some …

0. Introduction. Renaud [5] recently has extended the classic Mean and Individual Ergodic
Theorems to the framework of a-compact amenable locally compact unimodular groups. In …

In looking for generalizations of the classical individual ergodic theorem, weighted averages
have often been considered. In Rosenblatt [17], it was shown that given any countable group …

This concise classic by Paul R. Halmos, a well-known master of mathematical exposition,
has served as a basic introduction to aspects of ergodic theory since its first publication in …

Let G be a countably infinite group. Let (X, fl, m) be a probability space on which G acts as a
group of measure-preserving transformations. The action of G is ergodic if whenever A~ fl …

1. Introduction. Throughout this paper the term'probability space'will denote a nonatomic
Lebesgue probability space. Let G be a countable group,(X, 8, It) a probability space, and let …

Conditions are found on a sequence of probability measures ${\mu _n} $ on a locally
compact abelian group G so that, for any strongly continuous unitary representation of G …

We present a general new method for constructing pointwise ergodic sequences on
countable groups which is applicable to amenable as well as to non-amenable groups and …