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  "body": "\n## Summary\n\nA subset of a measurable space is universally measurable if it is measurable for the completion of every probability measure on the space.\nThe universally measurable sets form a σ-algebra that contains all the original measurable sets.\nIn Polish spaces they include the analytic sets, which may fail to be Borel.\n\n## Explanations\n\n### L1 human\n\nA set may fail to be in the original σ-algebra and still be harmless for every measure one could put on the space.\nUniversally measurable sets are those sets: whatever probability measure one chooses, the set differs from a measurable set by a negligible piece.\nEvery Borel subset of the real line is universally measurable.\nA Vitali set is not, because it is not measurable for Lebesgue measure on $[0, 1]$.\n",
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