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An Introduction to Ergodic Theory (Graduate Texts in Mathematics)
ISBN 0387951520 / 9780387951522 / 0-387-95152-0
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The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics. [via]