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  "body": "\n## Summary\n\nA Choquet capacity is a monotone set function defined on all subsets of a space.\nIt is continuous along increasing sequences of sets and along decreasing sequences of compact sets.\nChoquet introduced the notion to treat [[Newtonian capacity|4YZVFGJVSZ]] and outer measures in one framework.\nIts main result, Choquet's capacitability theorem, says that analytic sets can be approximated from inside by compact sets for every Choquet capacity.\nThis theorem is a basic tool for measurability questions in probability and descriptive set theory.\n\n## Explanations\n\n### L1 human\n\nA measure adds up sizes of disjoint pieces, but many useful notions of size do not add.\nA Choquet capacity asks only for three softer things.\nA bigger set is not smaller.\nGrowing sets have sizes that grow to the size of the limit.\nShrinking compact sets have sizes that shrink to the size of the limit.\nThe outer measure of a finite measure is an example, and so is the diameter of a set in a metric space.\n",
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