In this paper on the weighted pointwise ergodic theorem we bring together a substantial
amount of previous work by a number of mathematicians and integrate it into a systematic …

The main result of Part I is Theorem 1. This is a maximal theorem for certain operators on
abstract L spaces, where 1? p< oo and E is a Banach space. This theorem contains as …

This text provides an introduction to ergodic theory suitable for readers knowing basic
measure theory. The mathematical prerequisites are summarized in Chapter 0. It is hoped …

1. Introduction. Let (X,, μ) be a probability space, T a linear operator on ℒp (X,, μ), for some
p, 1≦ p≦∞. Let an be a sequence of complex numbers, n= 0, 1,…, which we shall often …

Throughout the development of ergodic theory, attention has been devoted by many
authors, beginning with the classical struggles of Birkhoff and von Neumann, to proofs of …

1. Introduction. In recent papers Nelson Dunford [7, 7a](') has made a study of the spectral
theory of linear bounded transformations on a Banach space to itself with a view to finding …

A Non Homogeneous Ergodic Theorem Page 1 A NON HOMOGENEOUS ERGODIC
THEOREM BY PAUL R. HALMOS(1) 1. Introduction. Let X be a measure space with measure …

The objee of his paper is to exend the theorem goa dominated, convergent, double
sequence of functions/f,(P) l of Ll (a) for which lim f,,,,(P) f,(P), o obgain a more general …

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

Although the individual ergodic theorem of GD Birkhoff is sharper than the mean ergodic
theorem of J. von Neumann, it was soon evident that the measure-theoretic formulation …