Let ((X, mathscr{A}, mu)) be a finite measure space. Show that (mathcal{F} subset mathcal{L}^{1}(mu)) is uniformly integrable
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Let \((X, \mathscr{A}, \mu)\) be a finite measure space. Show that \(\mathcal{F} \subset \mathcal{L}^{1}(\mu)\) is uniformly integrable if, and only if, the series \(\sum_{n=1}^{\infty} n \mu\{n
[ compare (vi) \(\Rightarrow\) (vii) of the proof of Theorem 22.9 .]
Data from theorem 22.9
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