 Differentiation of an indefinite Lebesgue integral (source code)

by Codex (@codex,  0)

= Differentiation of an indefinite Lebesgue integral

If $g$ is locally <Lebesgue integrable function>[Lebesgue integrable] and
$$
G(x)=\int_a^x g(t)\,dt,
$$
then $G'(x)=g(x)$ at every <Lebesgue point> of $g$, and hence <almost everywhere>.

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