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An outline of ergodic theory

Kalikow, Steven, (1950-)

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An outline of ergodic theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An outline of ergodic theory/ Steven Kalikow, Randall McCutcheon.
作者:	Kalikow, Steven,
其他作者:	McCutcheon, Randall,
出版者:	Cambridge :Cambridge University Press, : 2010.,
面頁冊數:	viii, 174 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Machine generated contents note: Preface; Introduction; 1. Measure-theoretic preliminaries; 2. Measure preserving systems, stationary processes; 3. Martingales and coupling; 4. Entropy; 5. Bernoulli transformations; 6. Ornstein isomorphism theorem; 7. Varieties of mixing; Appendix; References; Index.
標題:	Ergodic theory. -
電子資源:	https://doi.org/10.1017/CBO9780511801600
ISBN:	9780511801600

An outline of ergodic theory
Kalikow, Steven,1950-

An outline of ergodic theory[electronic resource] /Steven Kalikow, Randall McCutcheon. - Cambridge :Cambridge University Press,2010. - viii, 174 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;122. - Cambridge studies in advanced mathematics ;122..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Machine generated contents note: Preface; Introduction; 1. Measure-theoretic preliminaries; 2. Measure preserving systems, stationary processes; 3. Martingales and coupling; 4. Entropy; 5. Bernoulli transformations; 6. Ornstein isomorphism theorem; 7. Varieties of mixing; Appendix; References; Index.

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.

ISBN: 9780511801600Subjects--Topical Terms:

555691
Ergodic theory.

LC Class. No.: QA313 / .K35 2010

Dewey Class. No.: 515.48

An outline of ergodic theory
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 8 $a Machine generated contents note: Preface; Introduction; 1. Measure-theoretic preliminaries; 2. Measure preserving systems, stationary processes; 3. Martingales and coupling; 4. Entropy; 5. Bernoulli transformations; 6. Ornstein isomorphism theorem; 7. Varieties of mixing; Appendix; References; Index.
520 $a 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.
650 0 $a Ergodic theory. $3 555691
650 0 $a Isomorphisms (Mathematics) $3 705279
700 1 $a McCutcheon, Randall, $d 1965- $3 716629
830 0 $a Cambridge studies in advanced mathematics ; $v 122. $3 3470403
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