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YCor
YCor
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What kind Probability space with countable subset such that every subset of condition is this?positive measure meets the subset

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user64494
user64494
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What kind of condition is this: $\exists$ countable $K \subseteq X$ s.t. $\forall A \subseteq X$, $P(A) > 0 \implies A \cap K \ne \emptyset$?

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dohmatob
dohmatob
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What kind of condition is this: $\exists$ countable $K \subseteq X$ s.t. $\forall A \subseteq X$, $P(A) > 0 \implies A \cap K \ne \emptyset$

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

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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.