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  "body": "\n## Summary\n\nThe Lévy–Prokhorov metric is a distance between Borel [[probability measures|059TJN0NZ1]] on a [[metric space|0VKD1TP7F3]].\nTwo measures are close when each gives to every set little more mass than the other gives to a slight enlargement of it.\nOn a separable metric space, convergence in this metric is the same as [[weak convergence|MBW9JCGZC1]].\nSo weak convergence of probability measures comes from a metric.\n\n## Explanations\n\n### L1 human\n\nMoving mass a short distance should count as a small change, and so should changing a small amount of mass.\nThe Lévy–Prokhorov distance allows both kinds of error at once, with the same tolerance $\\varepsilon$.\nFor two point masses at $x$ and $y$, the distance is the smaller of $d(x, y)$ and $1$.\nSo point masses at $1/n$ and at $0$ are at distance $1/n$, which tends to $0$.\n",
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