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 …

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 …

Publisher Summary It was felt for a long time that martingales and ergodic theory, being
essentially theories of integration in infinitely many variables, should be obtainable from a …

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 …

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 …

On multiparameter ergodic and martingale theorems in infinite measure spaces Page 1
Probab. Th. Rel. Fields 71,477-490 (1986) Probability Theory=-~ 9 Spr~nger-Verlag 1986 On …

In many areas of analysis, ergodic theory and probability, square functions have proven to
be one ofthe most useful toolsto study convergence properties.(See the paper by Stein [17] …

Random markov processes and uniform martingales Page 1 ISRAEL JOURNAL OF
MATHEMATICS, Vol. 71, No. 1, 1990 RANDOM MARKOV PROCESSES AND UNIFORM …

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 …

Introduction. The purpose of this note is to show that for transformations in a Lebesgue
space L (S)(where S has finite measure) of the type Tf= f (kt)(where 4 is a map of S into all or …