Tail characterization of the Pinsker sigma-algebra
= Tail characterization of the Pinsker sigma-algebra
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A set belongs to the <Pinsker sigma-algebra> exactly when, modulo a null set, it belongs to $\mathcal T(\xi)$ for some finite measurable partition $\xi$. For a zero-entropy binary partition one may take that partition itself: zero conditional entropy makes its present atom measurable from every remote future.