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  "body": "\n## Summary\n\nThe Wasserstein metric is a distance between [[probability measures|059TJN0NZ1]] on a [[metric space|0VKD1TP7F3]].\nIt is the least cost of moving one mass distribution onto the other.\nThe cost of moving a unit of mass is a power of the distance it travels.\nIt is the central distance of optimal transport, and it metrizes weak convergence together with convergence of moments.\n\n## Explanations\n\n### L1 human\n\nThink of one measure as a pile of earth and the other as a hole of the same volume.\nA transport plan says how much earth goes from each place to each other place.\nThe Wasserstein distance is the cheapest total cost of such a plan.\nThis is why the $1$-Wasserstein distance is also called the earth mover's distance.\nFor two point masses at $x$ and $y$, all the mass must travel from $x$ to $y$, so the distance is $d(x, y)$.\n",
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