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  "body": "\n## Summary\n\nLet $f$ be a locally integrable function on $\\R^n$.\nA Lebesgue point of $f$ is a point $x$ where the average of $\\abs{f - f(x)}$ over small balls around $x$ tends to $0$.\nAt such a point, $f$ is well represented by its value $f(x)$ in an averaged sense.\nBy the Lebesgue differentiation theorem, almost every point is a Lebesgue point.\nPoints of continuity are Lebesgue points, but Lebesgue points need not be points of continuity.\n\n## Explanations\n\n### L1 human\n\nZoom into a function near a point and look at the average distance between $f$ and its value at the point.\nIf this average distance goes to zero as the window shrinks, the point is a Lebesgue point.\nFor the step function equal to $0$ on the negative numbers and $1$ elsewhere, the jump point $0$ is not a Lebesgue point.\nOn each small window around $0$ half of the values differ from $f(0) = 1$ by $1$.\n",
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