On the random ergodic theorem
نویسندگان
چکیده
منابع مشابه
A Vector-valued Random Ergodic Theorem
2. Theorem. Let £ be a reflexive B-space and let (S, 2, m) be a a-finite measure space. Let there be defined on S a strongly measurable function Ts with values in the B-space B(H) of bounded linear operators on H. Suppose that || 7\|| ^=1 for all sES. Let h be a measure-preserving transformation (m.p.t.) in (S, 2, m). Then for each XELi(S, £) there is an XELi(S, X) such that limn<„ «_1E"=i T*Th...
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With these assumptions we have T defined for every integer n as a 1-1, onto, bimeasurable transformation. Henceforth we shall assume that every set considered is measurable, i.e. an element of a. We shall say that P is invariant if P(A) =P(TA) for every set A, P is ergodic if P is invariant and if P(U^L_oo TA) = 1 for every set A for which P(A) > 0 , and finally P is strongly mixing if P is inv...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1977
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-61-3-231-237