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  "body": "\n## Summary\n\nThe restriction of a [[measure|PR11BZQQPG]] to a measurable set $A$ keeps the mass that lies inside $A$ and forgets the rest.\nIt is again a measure on the same space.\nRestriction lets one integrate over a subset, since the integral of $f$ over $A$ is the integral of $f$ for the restricted measure.\n\n## Explanations\n\n### L1 human\n\nPicture a measure as paint spread over a space.\nRestricting it to a region $A$ wipes away all the paint outside $A$.\nA set $B$ then gets the amount of paint that lies in both $B$ and $A$.\nFor example, restrict length on the real line to $A = [0, 1]$.\nThen the interval $[0, 5]$ gets the value $1$, and the interval $[2, 3]$ gets the value $0$.\n",
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