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Keywords:
ergodic transformation; strongly mixing; Birkhoff ergodic theorem; Komlós theorem
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 $\frac{1}{K} \sum _{k=1}^K f(T_{n_k}) \longrightarrow \int f \mathrm{d}P$ almost surely for all (or “many”) integrable $f$.
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