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Let $f$ be continous on $[a,b]$ and differentiable a.e. on $(a,b)$. Suppose there is a non-negative

function $g$ integrable on $[a,b]$ and $|\displaystyle \frac{f(x+1/n)-f(x)}{1/n}|\leq g$ a.e on $[a,b]$ for all $n$.

How can I show that: $\quad\displaystyle\int_a^bf'=f(b)-f(a). $

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    @Bunny: Maybe you could use one of the convergence theorems (for integrals). Can you think of one that might help?2012-12-03

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