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  "body": "\n## Summary\n\nA π-system on a set is a nonempty family of subsets that is closed under intersections of two members.\nIt is the kind of generating family used in the uniqueness theorems of measure theory.\nTwo probability measures that agree on a π-system agree on the σ-algebra it generates.\n\n## Explanations\n\n### L1 human\n\nA π-system is a family of sets in which the overlap of any two members is again a member.\nThe rays $(-\\infty, a]$ on the real line are the key example: the overlap of two rays is the shorter one.\nThese rays generate all Borel sets.\nSo a probability distribution on the line is fixed by its values on the rays, which is why a distribution function determines the distribution.\n",
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