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  "body": "\n## Summary\n\nA property holds quasi-everywhere on a set if it holds at every point outside a set of [[capacity zero|W9N1TR1X8P]].\nIt plays the role in potential theory that \"almost everywhere\" plays in measure theory, with capacity in place of measure.\nSince sets of capacity zero have Lebesgue measure zero, a property that holds quasi-everywhere also holds almost everywhere.\nMany results, such as [[Frostman's theorem|TX0Z2VVKH3]] and the solvability of the Dirichlet problem at boundary points, hold quasi-everywhere but not everywhere.\n\n## Explanations\n\n### L1 human\n\n\"Almost everywhere\" allows exceptions on a set of zero volume, which can still be quite large, like a whole line in the plane.\n\"Quasi-everywhere\" allows only exceptions on a set of capacity zero, which is much thinner.\nFor example, the potential of the equilibrium charge on a conductor is constant at every point of the conductor except on a set of capacity zero.\nSo quasi-everywhere statements are sharper than almost-everywhere statements.\n",
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