Im not entirely sure what this definition means, whilst I'm reading up.
Let $X_n \in$ some sigma algebra $\mathcal{F}$.
$X_n \uparrow X = X_n \subseteq X_{n+1}, \forall n \in \mathbb{N}$ and $\cup X_n = X.$
All that was written in my notes was the above line (which seems to be conditions?) But does $X_n \uparrow X$ mean that $X_n$ converges to $X$?