What does $X \in \mathbb{F}$ mean for $\mathbb{F}$ being a filtration

Question

I am reading lecture notes which say

Let $\mathbb{F}$ be a history, the process $X$ satisfies $X \in \mathbb{F}$ and ...

Now, I know what a history/filtration is, X is, in my understanding, a sequence of random variables. How can I say $X\in\mathbb{F}$? What does it mean?

In general, how can I say that a random variable lies in a sigma algebra?