Assume that a function [itex]f:[a,b]\to\mathbb{R}[/itex] is differentiable at all points in [itex][a,b][/itex] (we accept left and right sided derivatives at the end points). Will(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int\limits_{[a,b]}f'(x)dm_1(x) = f(b)-f(a)\quad\quad\quad\quad (1)

[/tex]

hold, where the integral is the Lebesgue integral?

Now, becareful with this thing. I know it looks simple, but I was unable to find an answer after going through my pedagogical material. The question contains different assumptions than the most commonly known theorems.

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# Integral of derivative

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