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Titlebook: Basic ergodic theory; M. G. Nadkarni Book 2013Latest edition Hindustan Book Agency (India) 2013

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樓主
發(fā)表于 2025-3-21 18:03:59 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Basic ergodic theory
影響因子2023M. G. Nadkarni
視頻videohttp://file.papertrans.cn/182/181020/181020.mp4
學(xué)科分類Texts and Readings in Mathematics
圖書封面Titlebook: Basic ergodic theory;  M. G. Nadkarni Book 2013Latest edition Hindustan Book Agency (India) 2013
影響因子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 the 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 level before their measure-theoretic or topological versions are presented. In addition, topics around the Glimm-Effros theorem are discussed. In the third edition a chapter entitled ‘Additional Topics‘ has been added. It gives Liouville‘s Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden‘s theorem on arithmetical progressions.
Pindex Book 2013Latest edition
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沙發(fā)
發(fā)表于 2025-3-21 23:04:22 | 只看該作者
eorem are discussed. In the third edition a chapter entitled ‘Additional Topics‘ has been added. It gives Liouville‘s Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden‘s theorem on arithmetical progressions.978-93-86279-53-8
板凳
發(fā)表于 2025-3-22 03:05:38 | 只看該作者
地板
發(fā)表于 2025-3-22 04:53:30 | 只看該作者
basic measure theory and metric topology. A new feature of the book is that the 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 th
5#
發(fā)表于 2025-3-22 08:49:05 | 只看該作者
6#
發(fā)表于 2025-3-22 12:54:08 | 只看該作者
Henry E. Kyburg, Jr. & Isaac Levi Srivatsa to give a measure free proof of the pointwise ergodic theorem. Application of Ramsay-Mackey theorem and some classical measure theory then provides us with an invariant probability measure when the space is incompressible. We will also briefly mention generalisations to Polish group actions.
7#
發(fā)表于 2025-3-22 20:45:56 | 只看該作者
Induced Automorphisms and Related Concepts,formation” (“induced automorphism”) by S. Kakutani who also studied its properties and used it to define a new kind of equivalence among the measure preserving automorphisms, now called Kakutani equivalence. In our exposition below of these concepts we will partly follow N. Friedman [2] who made these and related ideas available to a wider public.
8#
發(fā)表于 2025-3-22 21:58:12 | 只看該作者
9#
發(fā)表于 2025-3-23 03:18:36 | 只看該作者
Southern Africa and the , Maps,omorphisms are also metrically isomorphic has a negative answer. However in some special cases the answer is affirmative. One such situation is when . and . admit a complete set of eigenfunctions, . and . being ergodic and defined on a standard probability space.
10#
發(fā)表于 2025-3-23 05:40:05 | 只看該作者
Discrete Spectrum Theorem,omorphisms are also metrically isomorphic has a negative answer. However in some special cases the answer is affirmative. One such situation is when . and . admit a complete set of eigenfunctions, . and . being ergodic and defined on a standard probability space.
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