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In this Theorem, is it still true with assumption that the function g is not integrable. My answer is not, but I do not have a counter example. Any help will be appreciated

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  • $\begingroup$ What do you mean by g? $\endgroup$ – Olivier Moschetta Dec 13 '16 at 15:45
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Consider $f_n=\chi_{(n,n+1)}$. Then $|f_n|\le 1$. $f_n\to 0$ pointwise. But $\int f_n~dx=1$ for all $n$.

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