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  "body": "\n## Summary\n\nThe Lelong number of a [[plurisubharmonic function|FF2P7ER3QT]] $u$ at a point $x$ measures how fast $u$ tends to $-\\infty$ near $x$, compared with $\\log \\abs{z - x}$.\nThe same name is used for the analogous density of a closed [[positive current|BYJHP6A906]] at a point.\nFor $u = \\log \\abs{f}$ with $f$ holomorphic, the Lelong number is the order of vanishing of $f$ at $x$.\nLelong numbers are the basic local invariant of singularities in pluripotential theory.\n\n## Explanations\n\n### L1 human\n\nA plurisubharmonic function may have poles where it equals $-\\infty$.\nThe Lelong number tells how strong such a pole is, on a logarithmic scale.\nThe function $\\log \\abs{z}$ on $\\C$ has Lelong number $1$ at $0$, and $\\log \\abs{z^3} = 3 \\log \\abs{z}$ has Lelong number $3$.\nAt a point where the function is finite, the Lelong number is $0$.\n",
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  "name": "Lelong number",
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  "url": "https://tamnd.github.io/math2/wiki/lelong-number/",
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