Show that (int|u|^{p} d mu

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Show that \(\int|u|^{p} d \mu<\infty\) implies that \(|u|\) is a.e. real-valued (in the sense \((-\infty, \infty)\)-valued!). Is this still true if we have \(\int \arctan (u) d \mu<\infty\) ?

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