Fundamental theorem of calculus

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- Fundamental theorem of calculus for Lebesgue integration Fundamental theorem of calculus

Fundamental theorem of calculus for Lebesgue integration

If

g \in L^{1} (a, b)

, then

F (x) = F (a) + \int_{a}^{x} g (s) d s

is absolutely continuous and satisfies

F^{'} = g

almost everywhere. Conversely, every absolutely continuous function has this form.

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