Basic ergodic theory [electronic resource] / M.G. Nadkarni.

Call Number	515.42
Author	Nadkarni, M.G.
Title	Basic ergodic theory M.G. Nadkarni.
Edition	1st ed.
Physical Description	1 online resource (192 pages)
Series	Texts and Readings in Mathematics ; 6
Contents	Basic ergodic theory -- Contents -- Preface -- Chapter 1: Preliminaries and the Poincare Lemma -- Chapter 2: Ergodic Theorems of Birkhoff and von Neumann -- Chapter 3: Ergodicity -- Chapter 4: Mixing Conditions and Their Characterisations -- Chapter 5: Bernoulli Shift and Related Concepts -- Chapter 6: Discrete Spectrum Theorem -- Chapter 7: Induced Automorphisms and Related Concepts -- Chapter 8: Borel Automorphisms are Polish Homeomorphisms -- Chapter 9: The Glimm-Effros Theorem -- Chapter 10: E. Hopf's Theorem -- Chapter 11: H. Dye's Theorem -- Chapter 12: Flows and Their Representations -- Index.
Summary	This is an introductory text 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 the basic topics of ergodic theory such as the Poincaré 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 level before their measure -theoretic or topological versions are presented. In addition, topics centering around the Glimm-Effros theorem, which have so far not found a place in texts on ergodic theory are discussed in this book.
Subject	MATHEMATICS. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000031.html

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$a Basic ergodic theory -- Contents -- Preface -- Chapter 1: Preliminaries and the Poincare Lemma -- Chapter 2: Ergodic Theorems of Birkhoff and von Neumann -- Chapter 3: Ergodicity -- Chapter 4: Mixing Conditions and Their Characterisations -- Chapter 5: Bernoulli Shift and Related Concepts -- Chapter 6: Discrete Spectrum Theorem -- Chapter 7: Induced Automorphisms and Related Concepts -- Chapter 8: Borel Automorphisms are Polish Homeomorphisms -- Chapter 9: The Glimm-Effros Theorem -- Chapter 10: E. Hopf's Theorem -- Chapter 11: H. Dye's Theorem -- Chapter 12: Flows and Their Representations -- Index.

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$a Access restricted to authorized users and institutions.

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$a This is an introductory text 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 the basic topics of ergodic theory such as the Poincaré 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 level before their measure -theoretic or topological versions are presented. In addition, topics centering around the Glimm-Effros theorem, which have so far not found a place in texts on ergodic theory are discussed in this book.

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Summary	This is an introductory text 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 the basic topics of ergodic theory such as the Poincaré 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 level before their measure -theoretic or topological versions are presented. In addition, topics centering around the Glimm-Effros theorem, which have so far not found a place in texts on ergodic theory are discussed in this book.
Contents	Basic ergodic theory -- Contents -- Preface -- Chapter 1: Preliminaries and the Poincare Lemma -- Chapter 2: Ergodic Theorems of Birkhoff and von Neumann -- Chapter 3: Ergodicity -- Chapter 4: Mixing Conditions and Their Characterisations -- Chapter 5: Bernoulli Shift and Related Concepts -- Chapter 6: Discrete Spectrum Theorem -- Chapter 7: Induced Automorphisms and Related Concepts -- Chapter 8: Borel Automorphisms are Polish Homeomorphisms -- Chapter 9: The Glimm-Effros Theorem -- Chapter 10: E. Hopf's Theorem -- Chapter 11: H. Dye's Theorem -- Chapter 12: Flows and Their Representations -- Index.
Subject	MATHEMATICS. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000031.html