abandon
发表于 2025-3-21 18:03:59
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仔细阅读
发表于 2025-3-21 23:04:22
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
幻想
发表于 2025-3-22 03:05:38
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分离
发表于 2025-3-22 04:53:30
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
跑过
发表于 2025-3-22 08:49:05
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竖琴
发表于 2025-3-22 12:54:08
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.
mucous-membrane
发表于 2025-3-22 20:45:56
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 who made these and related ideas available to a wider public.
hemoglobin
发表于 2025-3-22 21:58:12
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繁荣中国
发表于 2025-3-23 03:18:36
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.
parsimony
发表于 2025-3-23 05:40:05
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.