Let ((X, mathscr{A}, mu)) be a (sigma)-finite measure space and (left(u_{n}ight)_{n in mathbb{N}} subset mathcal{M}(mathscr{A})). Show that

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Let \((X, \mathscr{A}, \mu)\) be a \(\sigma\)-finite measure space and \(\left(u_{n}ight)_{n \in \mathbb{N}} \subset \mathcal{M}(\mathscr{A})\). Show that \(u_{n} ightarrow u\) \((n ightarrow \infty)\) in measure if, and only if, \(u_{n}-u_{k} ightarrow 0(k, n ightarrow \infty)\) in measure.

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