An Outline of Ergodic Theory
Steven Kalikow Β· Randall McCutcheon
ΠΌΠ°ΡΡ 2010β―Π³. Β· Cambridge Studies in Advanced Mathematics ΠΠ½ΠΈΠ³Π°Β 122 Β· Cambridge University Press
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
183
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
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ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
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 ShannonβMcMillanβBreiman 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.
ΠΠ± Π°Π²ΡΠΎΡΠ΅
Steven Kalikow is a Visiting Professor in the Department of Mathematical Sciences at the University of Memphis.
Randall McCutcheon is Assistant Professor in the Department of Mathematical Sciences at the University of Memphis.
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