- #1
jostpuur
- 2,116
- 19
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
[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.
[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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