作者: 仔細(xì)閱讀 時(shí)間: 2025-3-21 23:04
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作者: 幻想 時(shí)間: 2025-3-22 03:05 作者: 分離 時(shí)間: 2025-3-22 04:53
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作者: 跑過(guò) 時(shí)間: 2025-3-22 08:49 作者: 豎琴 時(shí)間: 2025-3-22 12:54
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.作者: mucous-membrane 時(shí)間: 2025-3-22 20:45
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.作者: hemoglobin 時(shí)間: 2025-3-22 21:58 作者: 繁榮中國(guó) 時(shí)間: 2025-3-23 03:18
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.作者: parsimony 時(shí)間: 2025-3-23 05:40
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.作者: evaculate 時(shí)間: 2025-3-23 12:54 作者: Keshan-disease 時(shí)間: 2025-3-23 14:37 作者: 紳士 時(shí)間: 2025-3-23 20:50 作者: mosque 時(shí)間: 2025-3-23 22:20
Toponyms in Arabia, Syria, and Mesopotamia,sm on ., where . denotes the . ideal generated by the class of sets in . wandering under .,(See Chapter 1). This map was given the name “induced transformation” (“induced automorphism”) by S. Kakutani who also studied its properties and used it to define a new kind of equivalence among the measure p作者: 嚴(yán)厲批評(píng) 時(shí)間: 2025-3-24 05:16 作者: cultivated 時(shí)間: 2025-3-24 09:33 作者: motor-unit 時(shí)間: 2025-3-24 14:06 作者: 飲料 時(shí)間: 2025-3-24 17:00
Theil’s Work History and Biographical DataLet . be a non-empty set. A .-algebra . on . is a non-empty collection of subsets of . which is closed under countable unions and complements. A set together with a .-algebra . is called a Borel space or a Borel structure (., .).作者: Coeval 時(shí)間: 2025-3-24 19:33 作者: barium-study 時(shí)間: 2025-3-25 03:13
Theil’s Work History and Biographical DataA measure preserving Borel automorphism . on a probability space (., ., .) is said to be ergodic if for every . ∈ . invariant under ., .(.) = 0 or .(. ? .) = 0.作者: murmur 時(shí)間: 2025-3-25 04:59
,Name / Herkunft / Lebensumst?nde / Bildung,We have seen that a measure preserving automorphism . on a probability space (., ., .) is ergodic if and only if for all ., . ∈ .,.. Two properties stronger than ergodieity discovered by Koopman and von Neumann [2] will now be discussed.作者: PAD416 時(shí)間: 2025-3-25 09:15 作者: capsaicin 時(shí)間: 2025-3-25 14:58
Henry E. Kyburg, Jr. & Isaac LeviLet (., .) be a standard Borel space. A group ., . ∈ ?, of Borel automorphisms on (., .) is called a jointly measurable flow, or simply a flow, if作者: oxidant 時(shí)間: 2025-3-25 17:37
https://doi.org/10.1007/978-94-009-7718-1Liouville’s theorem has its origin in classical mechanics. In its simplified version it gives a necessary and sufficient condition for a flow of homeomor-phisms on an open subset in ?. to be volume preserving. Following K. R. Parthasarathy [8] we give this version first, followed by a discussion of its version in classical mechanics.作者: 偶然 時(shí)間: 2025-3-25 22:47
,The Poincaré Recurrence Lemma,Let . be a non-empty set. A .-algebra . on . is a non-empty collection of subsets of . which is closed under countable unions and complements. A set together with a .-algebra . is called a Borel space or a Borel structure (., .).作者: HEED 時(shí)間: 2025-3-26 00:12 作者: 抱狗不敢前 時(shí)間: 2025-3-26 04:42
Ergodicity,A measure preserving Borel automorphism . on a probability space (., ., .) is said to be ergodic if for every . ∈ . invariant under ., .(.) = 0 or .(. ? .) = 0.作者: 財(cái)政 時(shí)間: 2025-3-26 11:17
Mixing Conditions and Their Characterisations,We have seen that a measure preserving automorphism . on a probability space (., ., .) is ergodic if and only if for all ., . ∈ .,.. Two properties stronger than ergodieity discovered by Koopman and von Neumann [2] will now be discussed.作者: aggrieve 時(shí)間: 2025-3-26 14:49 作者: 堅(jiān)毅 時(shí)間: 2025-3-26 16:51
Flows and Their Representations,Let (., .) be a standard Borel space. A group ., . ∈ ?, of Borel automorphisms on (., .) is called a jointly measurable flow, or simply a flow, if作者: 使害羞 時(shí)間: 2025-3-26 23:11
Additional Topics,Liouville’s theorem has its origin in classical mechanics. In its simplified version it gives a necessary and sufficient condition for a flow of homeomor-phisms on an open subset in ?. to be volume preserving. Following K. R. Parthasarathy [8] we give this version first, followed by a discussion of its version in classical mechanics.作者: BOAST 時(shí)間: 2025-3-27 03:41 作者: 隱士 時(shí)間: 2025-3-27 07:29
Hindustan Book Agency (India) 2013作者: 珍奇 時(shí)間: 2025-3-27 11:57 作者: 能得到 時(shí)間: 2025-3-27 13:48 作者: 模仿 時(shí)間: 2025-3-27 18:46
,H. Dye’s Theorem, admit Borel cross-sections. We will therefore assume in the rest of this chapter that . and . are free and their orbit spaces do not admit Borel cross-sections. The first important result on orbit equivalence was obtained by H. Dye [2] and the main aim of this chapter is to prove his theorem.作者: 有雜色 時(shí)間: 2025-3-28 01:25 作者: 出價(jià) 時(shí)間: 2025-3-28 03:17 作者: 外星人 時(shí)間: 2025-3-28 09:28
Bernoulli Shift and Related Concepts,hift and the related concept of .-automorphism at an elementary level. Bernoulli shifts provide us with examples of mixing measure preserving automorphisms. The discussion here follows closely the exposition in Patrick Billingsley [1].作者: 小樣他閑聊 時(shí)間: 2025-3-28 11:18
Discrete Spectrum Theorem,ivalent. Let us say that . and . are spectrally isomorphic if . and . are unitarily equivalent. If . and . are spectrally isomorphic and . is ergodic then . is ergodic, because . is ergodic if and only if 1 is a simple eigenvalue of . hence also of ., which in turn implies the ergodicity of .. Simil作者: 審問(wèn),審訊 時(shí)間: 2025-3-28 17:28 作者: 某人 時(shí)間: 2025-3-28 22:47
The Glimm-Effros Theorem, ., . = . only when . = . the identity of the group.) If . is a probability measure supported on an orbit of ., then clearly the .-action is ergodic with respect to .. Thus there always exists, in a trivial sense, a probability measure with respect to which the .-action is ergodic. But the . above i作者: 綠州 時(shí)間: 2025-3-29 01:18
,E. Hopf’s Theorem,n of incompressibility was already formulated by E. Hopf ([5], 1932). We will combine a refined form of this notion with certain observations of V. V. Srivatsa to give a measure free proof of the pointwise ergodic theorem. Application of Ramsay-Mackey theorem and some classical measure theory then p作者: cruise 時(shí)間: 2025-3-29 06:38
,H. Dye’s Theorem,t equivalent, i.e., for there to exist a Borel isomorphism .: . → . such that for all ., .(orb (., .)) = orb (.(.), .). Let us observe that if . and . are orbit equivalent and if . has an orbit of length . then so has . and vice versa; moreover the cardinality of the set of orbits of length . for . 作者: 左右連貫 時(shí)間: 2025-3-29 11:08
9樓作者: keloid 時(shí)間: 2025-3-29 12:36
9樓作者: Urologist 時(shí)間: 2025-3-29 18:31
10樓作者: motivate 時(shí)間: 2025-3-29 22:31
10樓作者: 帶子 時(shí)間: 2025-3-30 03:43
10樓作者: prick-test 時(shí)間: 2025-3-30 06:57
10樓
