Understanding the Definition of Stopping Times in Set Theory

[cappadonza]

Hi this is more of a set theory question really, I'm a bit confused,

say \mathcal{F} is collections of sets, and \mathcal{F}_n is a sequence of sub collections of sets and say B_{1}, B_{2} ... is a sequence of sets
what does the following mean \mathcal{S} = \{ A \in \mathcal{F} \colon A \cap B_{n} \in \mathcal{F}_n \forall n \in \mathbb{N} \}

for an element to be a member of the set \mathcal{S} which of the conditons must be statisfy
does this mean if A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{2} \in \mathcal{F}_2 ... then it belongs to the set or
does it mean all these conditons must be met of it to be a members of the set A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{1} \in \mathcal{F}_2 , \space A \cap B_{1} \in \mathcal{F}_3 ... for each B_{1}, B_{2} ...

 

[EnumaElish]

The first is the correct interpretation, if A \cap B_1\in\mathcal{F}_1 and A \cap B_2\in\mathcal{F}_2, etc., for all n = 1, 2,..., then A is in the collection.