A question naturally arising in dynamical systems is: does a flow {~ t} have the same
nonwandering set as most of the time t maps, ç) This and similar questions for recurrency …

N-oo n= O f is an integrable function. Can this statement be improved in case Q is a compact
topological space, T a suitable homeomorphism of? 2 with itself, and fa continuous function …

1. Introduction. Throughout this paper the term'probability space'will denote a nonatomic
Lebesgue probability space. Let G be a countable group,(X, 8, It) a probability space, and let …

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 …

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 …

ff(P)di Page 1 MATHEMATICS: E. HOPF COMPLETE TRANSITIVITY AND THE ERGODIC
PRINCIPLE By EBERHARD HOPF1 HARVARD COLLEGE OBSERVATORY Communicated …

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 …

The theory of measure preserving transformations and flows (a flow is a 1-parameter group
of measure preserving transformations) originated in the study of classical dynamical …

Section 1. Let M be a Borel space, and let H be a locally compact group which is separable
in the sense of the second axiom of countability. We shall assume that M is analytic (see …

These are notes of a one-semester introductory course on Ergodic Theory that I gave at the
University of Maryland in College Park during the fall of 1970. I assumed the audience had …