Q:

$E[X\mid F_n] \to X$ almost surely

I was reading on 
Convergence in distribution of conditional expectations
Let $X$ be integrable on $(\Omega, \mathcal{F}, P)$ and assume $\mathcal{F}_n \uparrow \mathcal{F}$. Then, 
$$E(X \mid \mathcal{F}_n) \to X \ \ \text{a.s.}$$
And I was wondering if this is claim is true? Is it a well known fact? Has the theorem a name?

A:

Yes, this is one version of Doob's martingale convergence theorem.

