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  "body": "\n## Summary\n\nConcentration of measure is a phenomenon of many high-dimensional [[metric spaces|0VKD1TP7F3]] with a [[probability measure|059TJN0NZ1]].\nOn such a space, almost all of the space lies close to every set of measure at least $1/2$.\nEquivalently, every [[Lipschitz|0AW1E6YTJY]] function is nearly constant, close to its median, outside a set of very small measure.\nThe sphere $S^{n-1}$ and the [[Gaussian measure|P0DV2TCH1N]] on $\\R^n$ are the model examples.\nMilman put the phenomenon forward in the local theory of Banach spaces.\nIt is now a basic tool in asymptotic convex geometry, probability, statistics and computer science.\n\n## Explanations\n\n### L1 human\n\nOn a sphere in very high dimension, almost all of the area lies near the equator, whichever equator one picks.\nSo if a set covers half the sphere, then a thin band around it already covers almost everything.\nIn the same way, a function that does not change too fast takes nearly the same value at almost every point.\nFor example, the average of many independent coin flips is very close to $1/2$ with overwhelming probability, because it depends only a little on each flip.\n",
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