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  "body": "\n## Summary\n\nThe analytic capacity of a compact set $K \\subset \\C$ measures how large a bounded holomorphic function on $\\C \\setminus K$ can be near infinity, see the [[definition|X252NY7CS1]].\nIt is zero exactly when $K$ is removable for bounded holomorphic functions.\nThe search for a geometric description of the sets of analytic capacity zero is the Painlevé problem.\n\n## Explanations\n\n### L1 human\n\nRemove a compact set $K$ from the plane and look at holomorphic functions on what is left that stay bounded by $1$ and vanish at infinity.\nIf $K$ is a single point, the only such function is $0$, so the point is too small to matter.\nIf $K$ is a disc of radius $r$, the function $r/z$ works, and the capacity is $r$.\nAnalytic capacity is a number that tells how big $K$ is from the point of view of such functions.\n",
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