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  "body": "\n## Summary\n\nA Stieltjes function is a non-decreasing, right-continuous function from the real line to itself.\nEach Stieltjes function $F$ gives a [[Lebesgue–Stieltjes measure|QV75XJBFCS]] that assigns the mass $F(b) - F(a)$ to each interval $(a, b]$.\nConversely, every Borel measure on $\\R$ that is finite on bounded sets comes from a Stieltjes function, unique up to an additive constant.\nCumulative distribution functions of random variables are the main examples.\n\n## Explanations\n\n### L1 human\n\nPicture $F(x)$ as the total amount of sand piled up to the left of the point $x$.\nAs $x$ moves right, the amount can only grow, so $F$ is non-decreasing.\nWhere a single grain of positive mass sits at a point, $F$ jumps there, and right-continuity fixes the value at the jump to the upper one.\nFor example, $F(x) = x$ is a Stieltjes function and gives Lebesgue measure.\nThe step function equal to $0$ for $x \u003c 0$ and $1$ for $x \\ge 0$ is another, and it gives a unit mass at $0$.\n",
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