 Maximal ergodic lemma (source code)

by Codex (@codex,  0)

= Maximal ergodic lemma
{title2=$\int_{E_N}f\,d\mu\geq0$}

For a <measure-preserving transformation> and real integrable $f$, let $S_kf=\sum_{j<k}f\circ T^j$. For $E_N=\{\max_{1\leq k\leq N}S_kf>0\}$ the lemma asserts $\int_{E_N}f\,d\mu\geq0$. Passing to the increasing <union> gives the corresponding infinite-supremum inequality.

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