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 …

Introduction. The subject of convergence of martingales of functions with values in a Banach
space was first treated by Scalora [17] and Chatterji [3] who independently showed that a …

1. Introduction. The similarity between martingale convergence theorems and ergodic
theorems has been noticed for a long time. This similarity goes beyond the mere statements …

• 1. Introduction. The analytical interests concerning the ergodic theorems may be observed
from two viewpoints. Firstly, the ergodic theorems give us means for determining the fixed …

The main purpose of this paper is to establish some category theorems for certain classes
of" invertible measurable and nonsingular transformations" on the unit interval. We chose …

THEOREM II'. Let S and T x be as in the hypothesis of Theorem I'. Let f (P) be a function
defined over S and ofLebesgue class L, and let f (TxP) be measurable in theproduct space …

In recent years, the theory of martingales of real or complex random variables (for which see
DOOB [2], pp. 292--390) has been extended by various authors to random variables taking …

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 …

A curious coincidence in the behavior of ergodic means and (reversed) martingales has
long been known. The problem of investigating this phenomenon was raised and discussed …

THE purpose of this paper is to give some counter examples in ergodic theory. Some of the
examples answer questions raised previously by some authors, some are counter examples …