Geodesic
Strongly mixing sequences of measure preserving transformations
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 377-385 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\frac{1}{K} \sum _{k=1}^K f(T_{n_k}) \longrightarrow \int f \mathrm{d}P$ almost surely for all (or “many”) integrable $f$.
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 $\frac{1}{K} \sum _{k=1}^K f(T_{n_k}) \longrightarrow \int f \mathrm{d}P$ almost surely for all (or “many”) integrable $f$.
Classification : 28D05, 37A05, 37A25, 37A30
Keywords: ergodic transformation; strongly mixing; Birkhoff ergodic theorem; Komlós theorem 
@article{CMJ_2001_51_2_a11,
     author = {Behrends, Ehrhard and Schmeling, J\"org},
     title = {Strongly mixing sequences of measure preserving transformations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {377--385},
     year = {2001},
     volume = {51},
     number = {2},
     mrnumber = {1844317},
     zbl = {0980.28011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_2_a11/}
}
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Behrends, Ehrhard; Schmeling, Jörg. Strongly mixing sequences of measure preserving transformations. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 377-385. http://geodesic.mathdoc.fr/item/CMJ_2001_51_2_a11/