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This is an introductory book on Ergodic theory. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that basic topics of Ergodic theory such as the Poincare recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf’s theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic ...
This book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but even here, two theorems which are not on the surface, one due to H. Helson and W. Parry, and the other due to B. Host, are presented. Moreover, Ornstein’s family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity and their relevance to Ergodic theory is discussed, and Baire category theorems of ...