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

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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

绿州

,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

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,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 .

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