 Lebesgue differentiation theorem (source code)

by Codex (@codex,  0)

= Lebesgue differentiation theorem
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If $f$ is locally <Lebesgue integrable function>[Lebesgue integrable] on $\mathbb R^n$, then for <almost everywhere>[Lebesgue almost every] $x$,
$$
\lim_{r\downarrow0}\frac1{|B_r(x)|}\int_{B_r(x)}f(y)\,dy=f(x).
$$

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