Interpretation of Stopped $\sigma$-algebra I'm currently learning the definition of a stopped $\sigma$-algebra:

Let $T$ be a stopping time. We define the stopped $\sigma$-algebra $\mathcal{F}_T$ as
$$ \mathcal{F}_T := \{A \in \mathcal{F}\mid\forall n \in \mathbb{N}: A \cap \{T=n\}\in \mathcal{F}_n\}$$

My question is informal: How can this $\sigma$-algebra be interpreted in "the real world"? For example, what would $\mathcal{F}_T$ mean for a gambler?
Thank you already!

$\mathcal F_T$ is the information available up to time $T$.  The only difference here is that $T$ is a random (stopping) time.  For example, if a gambler playing a game until she goes broke and leaves, we could set $T$ to be the time she goes broke.  Then $\mathcal F_T$ would contain the results of all of the games she played.
It's hard to see that from the definition of $\mathcal F_T$, so it might help to write out $\mathcal F_T$ using the definition in a simple concrete example.  For example, look at the sample space of three coin tosses with the natural filtration and have $T$ be the first time the coin comes up heads.
