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  "body": "\n## Summary\n\nThe energy of a positive measure is the double integral of a potential-theoretic kernel against the measure in both variables.\nTypical kernels are $\\abs{x - y}^{2-n}$ in $\\R^n$ for $n \\ge 3$ and $\\log(1/\\abs{x - y})$ in the plane.\nPhysically it is the electrostatic energy of the charge distribution described by the measure.\nMinimising the energy over probability measures on a compact set defines its [[capacity|4YZVFGJVSZ]] and its equilibrium measure.\nSets that carry no nonzero measure of finite energy are the negligible sets of potential theory.\n\n## Explanations\n\n### L1 human\n\nSpread a unit of electric charge over a body.\nEvery pair of tiny bits of charge repels with an energy that grows as they get closer, and the energy of the measure adds up all these pair energies.\nA point charge has infinite energy, because the charge sits on top of itself.\nCharge spread evenly over the unit sphere in space has energy $1$ for the kernel $1/\\abs{x - y}$.\n",
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