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  "body": "\n## Definition\n\nLet $n \\ge 2$, let $A \\subseteq \\R^n$, and let $P$ be a property that each point of $A$ may or may not have.\nThe property $P$ holds *quasi-everywhere* on $A$, abbreviated q.e., if the set of points of $A$ where $P$ fails has [[capacity zero|W9N1TR1X8P]].\n\n## Remarks\n\nExample: let $K$ be the closed unit disc in $\\C$ and let $u(z) = \\log \\abs{z}$.\nThen $u \u003e -\\infty$ quasi-everywhere on $K$, since the exceptional set $\\set{0}$ is finite and so has capacity zero.\n\nNon-example: let $u$ be the function on $\\C$ with $u = 1$ on the segment $[0, 1]$ and $u = 0$ elsewhere.\nThen $u = 0$ almost everywhere with respect to area, but not quasi-everywhere, because the segment has positive logarithmic capacity.\n\nIn $\\R^n$ with $n \\ge 3$ the capacity used is the Newtonian capacity, and in the plane it is the logarithmic capacity.\nIn nonlinear potential theory one speaks of $p$-quasi-everywhere, with the $p$-capacity in place of the Newtonian capacity.\n",
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