Birkhoff's pointwise ergodic theorem: $\frac1n\sum_{k<n} f\circ T^k \to \mathbb E[f\mid\mathcal I]$ almost everywhere

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Birkhoff's pointwise ergodic theorem: $\frac1n\sum_{k<n} f\circ T^k \to \mathbb E[f\mid\mathcal I]$ almost everywhere · Prove2Me