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  "body": "\n## Summary\n\nA measure $\\nu$ is absolutely continuous with respect to a measure $\\mu$, written $\\nu \\ll \\mu$, when every $\\mu$-null set is also $\\nu$-null.\nBy the [[Radon–Nikodym theorem|1ZSZS5G1Q4]], for σ-finite measures this holds exactly when $\\nu$ has a density with respect to $\\mu$.\nIt is the measure-theoretic counterpart of the [[absolute continuity|ZT6F4C2YHK]] of functions.\nA nondecreasing function on a closed bounded interval is absolutely continuous exactly when its Lebesgue–Stieltjes measure is absolutely continuous with respect to Lebesgue measure.\nIn probability, random variables with a density are those whose law is absolutely continuous with respect to Lebesgue measure.\n\n## Explanations\n\n### L1 human\n\nAbsolute continuity of $\\nu$ with respect to $\\mu$ means that $\\nu$ never sees anything that $\\mu$ ignores.\nIf a set is negligible for $\\mu$, it is negligible for $\\nu$ too.\nThe normal distribution is absolutely continuous with respect to Lebesgue measure on $\\R$, since it is given by a density.\nA point mass at $0$ is not: the single point $\\set{0}$ has length $0$ but carries mass $1$.\n",
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