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

Question:

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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