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Strongly mixing sequences of measure preserving transformations. (English) Zbl 0980.28011

Summary: We call a sequence \((T_n)\) of measure preserving transformations strongly mixing if \(P(T_n^{-1}A\cap B)\) tends to \(P(A)P(B)\) for arbitrary measurable \(A\), \(B\). We investigate whether one can pass to a suitable subsequence \((T_{n_k})\) such that \(\frac 1K \sum_{k=1}^K f(T_{n_k}) \rightarrow \int f dP\) almost surely for all (or “many”) integrable \(f\).

MSC:

28D05 Measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
37A05 Dynamical aspects of measure-preserving transformations
37A30 Ergodic theorems, spectral theory, Markov operators
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References:

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