Let $(\Omega,\mathfrak{F})$ be a measurable space. When does there exist an injective measurable function $f:(\Omega,\mathfrak{F})\to (\mathbb{R}^n,B(\mathbb{R}^n))$ to some Euclidean space, here $B(\mathbb{R}^n)$ is the Borel $\sigma$-algebra.

Thoughts. Clearly, if $\Omega$ is a Riemannian manifold and $\mathfrak{F}$ is its Borel $\sigma$-algebra then this works but I'm thinking of more general, non-topological criteria. (If they exist)