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 …

Summary Let (Ω,⌆, P) be a probability space and let T be a measurable and measure
preserving point transformation from Ω into Ω. Let f be a measurable and square integrable …

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 …

Assume T is an ergodic measure preserving point transformation from a probability space
onto itself. Let be a sequence of pairs of positive integers, and define the sequence of …

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

1. Introduction. In this note we will prove a point-wise convergence theorem analogous to
the ergodic theorem, the novelty being that we use a system of weighted averages. The work …

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 …

Let T be a measure preserving transformation on a finite measure space. Then for certain
increasing sequences k 1 k 2,... of positive integers, called uniform sequences, the average …

BALANCING ERGODIC AVERAGES Brian Marcus (1) and Karl Petersen (2)].~ ckground
and results. We consider a (Lebesgue) probability sp; Jue(X, g, IA) and either a single …

Our purpose is to answer affirmatively the question considered in [Fu] on the almost sure
convergence of ergodic averages of the form where m is a fixed integer ΦΟ, l and T an …