Let $(X, \mathcal{A}, \mu)$ be a measure space, and let $f, f_1, f_2, \ldots : X \to \mathbb{R}$ be $\mathcal{A}$-measurable functions. Then $f_n \xrightarrow{\mu} f$ if and only if every subsequence of $(f_n)$ has a further subsequence that converges to $f$ pointwise $\mu$-a.e.