James E. Humphreys
Julius L. Shaneson
Lance Small (chair)
2000 Mathematics Subject Classification. Primary 28D20, 28D05, 94A17;
Secondary 60F05, 60G17, 94A24.
ABSTRACT. This book is about finite-alphabet stationary processes, which are important in physics,
engineering, and data compression. The book is designed for use in graduate courses, seminars or
self study for students or faculty with some background in measure theory and probability theory.
Library of Congress Cataloging-in-Publication Data
Shields, Paul C.
The ergodic theory of discrete sample paths / Paul C. Shields.
p. cm. — (Graduate studies in mathematics, ISSN 1065-7339; v. 13)
Includes bibliographical references and index.
ISBN 0-8218-0477-4 (alk. paper)
1. Ergodic theory. 2. Measure-preserving transformations. 3. Stochastic processes. I. Title.
QA313.S55 1996 96-20186
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Republication, systematic copying, or multiple reproduction of any material in this publication
is permitted only under license from the American Mathematical Society. Requests for such
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© 1996 by the American Mathematical Society. All rights reserved.
Reprinted by the American Mathematical Society, 2009.
The American Mathematical Society retains all rights
except those granted to the United States Government.
@ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.
Visit the AMS home page at http://www.ams.org/
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