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  "body": "\n## Summary\n\nThe Radon–Nikodym derivative $d\\nu / d\\mu$ is the density of one measure $\\nu$ with respect to another measure $\\mu$.\nIt exists when both measures are σ-finite and $\\nu$ is absolutely continuous with respect to $\\mu$, by the [[Radon–Nikodym theorem|1ZSZS5G1Q4]].\nIt turns integrals against $\\nu$ into integrals against $\\mu$.\nProbability densities, likelihood ratios and conditional expectations are all Radon–Nikodym derivatives.\n\n## Explanations\n\n### L1 human\n\nThink of $\\mu$ as a way to measure size and $\\nu$ as a way to measure mass.\nThe derivative $d\\nu / d\\mu$ at a point is the mass per unit size near that point.\nFor the standard normal distribution $\\nu$ and Lebesgue measure $\\mu$ on the line, the derivative is the bell curve $e^{-x^2/2}/\\sqrt{2\\pi}$.\nThe name comes from the rule $d\\nu = \\frac{d\\nu}{d\\mu} \\, d\\mu$, which looks like the chain rule of calculus.\n",
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