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Generalized commuting properties of measure-preserving transfomations [PDF]

open access: yesTransactions of the American Mathematical Society, 1965
Cn( T) -C Cn+1 (T), n = 0, 1, 29 If there exists an integer N such that CN(T) = CN+1(T) then Cn(T) = Cn+1(T) for all n ? N; and in this case we define N(T) = min{N: CN(T) = CN+1(T) }, otherwise we set N(T) = o. We call N(T) the generalized commuting order of T. If RT1R-1 = T2 a.e., where R, T1, T2 E G then it is clear that -N(T1) = N(T2), i.e., N(T) is
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Algebraic Models for Measure Preserving Transformations [PDF]

open access: yesTransactions of the American Mathematical Society, 1968
Dinculeanu, Nicolae, Foiaš, Ciprian
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Centralizer of an Ergodic Measure Preserving Transformation

open access: yesPublications of the Research Institute for Mathematical Sciences, 1982
§ 1. Let T be an ergodic measure preserving transformation of a Lebesgue measure space (Q, 23, P), P(O)=1, that is, Tis a one to one mapping from Q onto itself, bimeasurable (T9J = 93), measure preserving (P(T"1A) = P(A) for A in S3) and ergodic (every measurable function /(«) with f(Tco)=f((o) a.e. is constant a.e.).
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