Abstract
These notes develop a theory of restricted orbit equivalence
which has as particular examples Ornstein's isomorphism theorem
for Bernoulli processes, Dye's orbit equivalence theorem for ergodic
processes and the theory of Kakutani equivalence developed by
Feldman, Ornstein, Weiss and Katok. Other examples are also given.
A number of results from the Bernoulli theory are shown to be true
for any restricted orbit equivalence.
1980 Mathematics Subject Classification, Primary 28D05, 28D20.
Library of Congress Cataloging in Publication Data
Rudolph, Daniel J.
Restricted orbit equivalence.
(Memoirs of the American Mathematical Society, ISSN 0065-9266; no. 323)
"Volume 54, number 323 (fifth of 6 numbers)."
Bibliography: p.
1. Ergodic theory. 2. Entropy (Information theory) I. Title. II. Title: Orbit
equivalence. III. Series.
QA3.A57 no. 323 [QA313] 510s [515.4'2] 84-28119
ISBN 0-8218-2324-8
COPYING AND REPRINTING. Individual readers of this publication, and nonprofit
libraries acting for them, are permitted to make fair use of the material, such as to copy an
article for use in teaching or research. Permission is granted to quote brief passages from this
publication in reviews, provided the customary acknowledgement of the source is given.
Republication, systematic copying, or multiple reproduction of any material in this
publication (including abstracts) is permitted only under license from the American Mathe-
matical Society. Requests for such permission should be addressed to the Executive Director,
American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940.
The owner consents to copying beyond that permitted by Sections 107 or 108 of the
U.S. Copyright Law, provided that a fee of $1.00 plus $.25 per page for each copy be paid
directly to the Copyright Clearance Center, Inc., 21 Congress Street, Salem, Massachusetts
01970. When paying this fee please use the code 0065-9266/85 to refer to this publication.
This consent does not extend to other kinds of copying, such as copying for general distribu-
tion, for advertising or promotion purposes, for creating new collective works, or for resale.
iv
Previous Page Next Page