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- Jan 26, 2012

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**Problem**: Consider\[f_n = \begin{cases}1 & \forall\,x\in\left[n,n+1\right)\\ 0 & \forall\,x\in\mathbb{R}\backslash\left[n,n+1\right)\end{cases}\]

Show that

\[\int_{\mathbb{R}}\liminf_{n\to\infty}f_n\,dm < \liminf_{n\to\infty}\int_{\mathbb{R}}f_n\,dm.\]

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