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CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 122
Editorial Board
B. BOLLOBÁS, W. FULTON, A. KATOK, F. KIRWAN,
P. SARNAK, B. SIMON, B. TOTARO
AN OUTLINE OF ERGODIC THEORY
This informal introduction provides a fresh perspective on isomorphism theory, which
is the branch of ergodic theory that explores the conditions under which two
measure-preserving systems are essentially equivalent. It contains a primer in basic
measure theory, proofs of fundamental ergodic theorems, and material on entropy,
martingales, Bernoulli processes, and various varieties of mixing.
Original proofs of classic theorems – including the Shannon–McMillan–Breiman
theorem, the Krieger finite generator theorem, and the Ornstein isomorphism
theorem – are presented by degrees, together with helpful hints that encourage the
reader to develop the proofs on their own. Hundreds of exercises and open problems
are also included, making this an ideal text for graduate courses. Professionals needing
a quick review, or seeking a different perspective on the subject, will also value this
book.
STEVEN KALIKOW is a Visiting Professor in the Department of Mathematical
Sciences at the University of Memphis.
RANDALL MCCUTCHEON is Associate Professor in the Department of Mathematical
Sciences at the University of Memphis.
CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS
Editorial Board:
B. Bollobás, W. Fulton, A. Katok, F. Kirwan, P. Sarnak, B. Simon, B. Totaro
All the titles listed below can be obtained from good booksellers or from Cambridge University
Press. For plete series listing visit: ies/?code=CSAM
Already published
73 B. Bollobás Random graphs (2nd Edition)
74 R. M. Dudley Real analysis and probability (2nd Edition)
75 T. Sheil-plex polynomials
76 C. Voisin Hodge theory plex algebraic geometry, I
77 C. Voisin Hodge theory plex algebraic geometry, II
78 V. pletely bounded maps and operator algebras
79 F. Gesztesy & H. Holden Solit