Let $(X, \mathcal F, P)$ be a probability space.

Question

What kind of condition is this: there exists a sequence $(a_n)_n \subseteq X$ such that

$\forall$ measurable $A \subseteq X$, $P(A) > 0 \implies a_n \in A$ for some $n$.

Context. I'm reviewing a paper for a conference and the authors assume this condition on the probability space in order to prove a result. I was wondering if this condition has a technical name, etc. in the greater math literature.