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  "body": "\n## Summary\n\nA measurable space is a set together with a [[σ-algebra|0SV8K0TDGY]] of its subsets.\nThe sets in the σ-algebra are the measurable sets.\nMeasurable spaces are the setting in which measures, measurable functions and random variables are defined.\n\n## Explanations\n\n### L1 human\n\nA measurable space is a set with a chosen list of subsets that one is allowed to measure.\nThe list must contain the whole set and be stable under complements and countable unions.\nThink of a dartboard: one wants to speak of the probability of hitting a region, so one fixes which regions count.\nFor example, the real line with the Borel sets, generated by the open intervals, is a measurable space.\nNo measure is chosen yet; the measurable space only fixes which sets will get a size.\n",
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