What is the meaning of the symbol " $ \vee $" in this case?

Question

Let $(X_n)_n $ and $(Y_n)_n$ be two martingales with respect to natural filtrations
$ \mathcal{F}^X_s $ and $ \mathcal{F}^Y_s$ respectively. What is the meaning of the filtration $ \mathcal{F}^X_s\vee\mathcal{F}^Y_s$?

Source of the question: http://alexanderchernyy.com/pmt.pdf, theorem 2.1 page 4

Answer 1

For two $\sigma$-algebras $\mathcal{A}$ and $\mathcal{B}$ on the same set, one usually denotes

$$ \mathcal{A} \vee \mathcal{B} := \sigma(\mathcal{A}\cup\mathcal{B}).$$

This is a pretty common notation when talking about filtrations.

Answer 2

If $\ \mathcal{F}, \mathcal{G}\ $ are $\sigma$-algebras, then $\mathcal{F}\vee\mathcal{G}$ is the $\sigma$-algebra generated by $\ \mathcal{F}\cup\mathcal{G}\ $, known as the join of $\ \mathcal{F}\ $ and $\ \mathcal{G}\ $.