Suppose we have $f \in L(I)$ and derivative $f'$ exists almost everywhere . It is $f'$ measurable ? I have no idea how to begin to construct the proof .
2026-04-28 01:36:11.1777340171
derivative of lebesgue integrable function
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You have that $f'(x) = \lim_{n\to +\infty} n(f(x+\frac{1}{n}) - f(x) )$ almost everywhere
So $f'$ is a simple limit of measurable functions hence measurable