Reference for a version of the Rellich-Kondrachov theorem for $L^1$ space into $BV$ space

Question

I'm reading a note about Modica-Mortola Functional.
On page3, the author claims that by the Rellich-Kondrachov theorem, for a bounded sequence $(u_n)\subset L^1(\Omega)$, we can find a subsequence $(u_{n_k})$ and a $u\in BV(\Omega)$ such that $$u_{n_k}\to u\mbox{ in }L_{loc}^{1}(\Omega).$$ Since the version of the Rellich-Kondrachov theorem I know is to compactly embede Sobolev spaces into some $L^p$ spaces, so I'm wondering if anyone can give any reference about this version.
Any clue would be welcome!