母牛胆小鬼 发表于 2025-3-21 16:53:39

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Crayon 发表于 2025-3-21 22:45:06

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Awning 发表于 2025-3-22 03:36:16

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SPASM 发表于 2025-3-22 07:04:57

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消灭 发表于 2025-3-22 09:32:19

M. N. Walsh,J. J. Hubert,E. M. CarterErgodicity, freeness, and Poincaré recurrence are the three most basic properties in ergodic theory, and not coincidentally they can all be motivated in analogy with the simple picture that describes arbitrary group actions on ordinary sets.

Urea508 发表于 2025-3-22 16:25:17

,Exploratory Data Analysis in “R”,As shown in Theorem ., every unitary representation . of a group on a Hilbert space decomposes uniquely into a sum of a weakly mixing representation and a compact representation. The weakly mixing and compact vectors each form a closed .-invariant subspace of ., and these subspaces are orthogonal and have direct sum equal to ..

Urea508 发表于 2025-3-22 17:25:01

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GRATE 发表于 2025-3-22 22:23:11

Microbial Biosurfactants and BiodegradationWhile the Koopman representation can be used to distinguish many types of p.m.p. actions, it cannot distinguish nontrivial Bernoulli actions over an infinite group, as one always gets infinitely many copies of the left regular representation, along with a copy of the trivial representation (see Section .).

bronchiole 发表于 2025-3-23 05:26:09

Susanne Zibek,Gloria Soberón-ChávezIn Section . we arrived at a definition of entropy for p.m.p. actions of amenable groups by combining a concept which is internal to the space (the Shannon entropy of a partition) with one which is internal to the group (the process of averaging over Følner sets).

oracle 发表于 2025-3-23 07:51:25

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查看完整版本: Titlebook: Ergodic Theory; Independence and Dic David Kerr,Hanfeng Li Book 2016 Springer International Publishing AG 2016 Ergodic Theory.Topological D