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 …

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 …

• 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 …

Let (X,(B, m) denote the measure space consisting of the unit interval with Lebesgue
measure. We let 3 denote the class of measurable nonsingular invertible transformations …

§ 0. Introduction. Let (X, M, X) be a finite or «--finite measure space. For the group M of
invertible, measure preserving transformations, or more ge ally for the group'S of invertible …

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 …

Introduction. Ergodic sets were introduced by Kryloff and Bogoliouboff in 1937 in connection
with their study of compact dynamical systems [16]. The purpose of this paper is to review …

Let X be a topological space, G a topological group with identity element e. Let f be a
continuous mapping from XXG into X. For simplicity we will write f (x, g) as xg. If (xg1) g2= x …

1. Introduction. The purpose of this paper is to review the progress made in the study of
measurable and measure preserving transformations during the last 17 years. The interest …

We shall be concerned with the basic problem of classifying measure preserving
transformations. For much of the background material the survey of Halmos [10] is adequate; …