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  "body": "\n## Summary\n\nThe Lelong class $\\mathcal{L}$ is the set of [[plurisubharmonic functions|FF2P7ER3QT]] on $\\C^n$ that grow at most like $\\log\\abs{z}$ at infinity.\nIt is the analogue, for functions, of the set of polynomials of bounded degree.\nFor every polynomial $p$ of degree $d \\ge 1$, the function $\\frac{1}{d} \\log\\abs{p}$ lies in $\\mathcal{L}$.\nThe [[Siciak extremal function|QBJ9R06GYE]] of a set is defined as an upper envelope of functions of the Lelong class.\nThe subclass $\\mathcal{L}^+$ of functions that also grow at least like $\\log\\abs{z}$ contains the regularised extremal functions of compact sets that are not pluripolar.\n\n## Explanations\n\n### L1 human\n\nA polynomial of degree $d$ grows like $\\abs{z}^d$, so its logarithm divided by $d$ grows like $\\log\\abs{z}$.\nThe Lelong class collects all plurisubharmonic functions with this kind of logarithmic growth.\nFor example, $\\log(1 + \\abs{z})$ and $\\max(\\log\\abs{z_1}, \\log\\abs{z_2})$ are in the Lelong class of $\\C^2$.\nThe function $\\abs{z_1}$ is plurisubharmonic but grows too fast, so it is not in the class.\n",
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