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  "body": "\n## Summary\n\nLebesgue–Stieltjes integration integrates a function $f$ against a non-decreasing function $g$ on the real line, written $\\int f \\, dg$.\nIt is the Lebesgue integral with respect to the Lebesgue–Stieltjes measure of $g$, which gives each interval $(a, b]$ the mass $g(b) - g(a)$.\nIt extends the Riemann–Stieltjes integral to all measurable functions, and to functions $g$ of bounded variation by splitting $g$ into monotone parts.\nIt is the language of probability distributions on the line, where $g$ is a cumulative distribution function.\n\n## Explanations\n\n### L1 human\n\nIn an ordinary integral each small piece of the line counts with its length.\nIn a Stieltjes integral it counts with the increase of a given function $g$ over that piece.\nWhere $g$ is flat, nothing is counted; where $g$ jumps, the point of the jump gets a mass equal to the jump.\nFor example, if $g$ jumps from $0$ to $1$ at $0$ and is constant elsewhere, then $\\int f \\, dg = f(0)$.\n",
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