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I need help showing that that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$ where $f$ is a nonegative measurable function. For the case that $f$ is integrable over ${\mathbb{R}}$ I think I solved using Lebesgue Dominated convergence Theorem on the sequence $f_n=f\chi_{[-n,n]}$. I have no idea how to proceed with the case $\int_{\mathbb{R}} f=\infty$

Any help would be greatly appreciated

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Hint: Try the monotone convergence theorem.

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  • $\begingroup$ yeah you are right we were studying the dominated convergence theorem in class and I forgot about the monotone. Thanks $\endgroup$ – TheGeometer Oct 29 '18 at 20:29

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