A well-known result in measure theory states that given a sequence $(f_n)_{n=1}^\infty$ of measurable functions from a $\sigma$-finite measure space $(X,\mathcal{A},\mu)$ to $\mathbb{R}$ then the sequence $(f_n)_{n=1}^\infty$ convergences in measure to a function $f$ if and only *every* subsequence $(f_{n_m})_{m=1}^\infty$ has a subsequence $(f_{n_{m_p}})_{p=1}^\infty$ which converges to $f$ almost everywhere.

By whom and where was this theorem originally proved?