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  "body": "\n## Summary\n\nA metric outer measure is an [[outer measure|BJ314H17HC]] on a [[metric space|0VKD1TP7F3]] with one extra property.\nIt is additive on any two sets lying at positive distance from each other.\nThis condition links the outer measure with the geometry of the space.\nIts main use is that for a metric outer measure every Borel set is measurable in the sense of Carathéodory.\nLebesgue outer measure and the [[Hausdorff outer measures|Q1TGZK8RN6]] are metric outer measures.\n\n## Explanations\n\n### L1 human\n\nIf two sets are separated by a gap, their total size should be the sum of their sizes.\nA metric outer measure is an outer measure that respects this rule.\nFor example, in the plane, two disks that do not touch have total area equal to the sum of their areas.\nThis simple rule is enough to make all open and closed sets measurable.\n",
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