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  "body": "\n## Summary\n\nA pluripolar set is a subset of $\\C^n$ that lies, at least locally, in the set where a [[plurisubharmonic function|FF2P7ER3QT]] takes the value $-\\infty$.\nPluripolar sets are the negligible sets of pluripotential theory, in the same way as [[polar sets|C95QJ7YH5T]] are the negligible sets of classical potential theory.\nThey have Lebesgue measure zero, and plurisubharmonic functions bounded above extend across closed pluripolar sets.\nBy [[Josefson's theorem|V6XSDT5C21]], a set that is pluripolar locally is pluripolar for one plurisubharmonic function on all of $\\C^n$.\n\n## Explanations\n\n### L1 human\n\nThe function $\\log\\abs{f}$ of a holomorphic function $f$ equals $-\\infty$ exactly where $f$ vanishes.\nSo the zero set of a holomorphic function, such as the complex line $z_1 = 0$ in $\\C^2$, is pluripolar.\nPluripolar sets are small sets: they cannot contain an open set, and they have volume zero.\nA countable union of pluripolar sets is again pluripolar, so the union of countably many complex lines is pluripolar.\nThe real line $\\R^n$ inside $\\C^n$ is not pluripolar, although it has volume zero.\n",
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