Suppose $T_k$ are measure perserving for each $k$, and $f$ is integrable. Is it true that $\frac{1}{n}\sum_{k=1}^n f(T_k\circ T_{k-1}\dots\circ T_1 \omega)$ converge almost surely?
2026-03-26 19:16:59.1774552619
A variation of Birkhoff's Ergodic theorem
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