What does "a.s." stand for? I was reading an article and I saw the following sentence:

For a given martingale, if it has an upper or a lower bound, then the
  martingale must converge (a.s.). Since the likelihood is always
  nonnegative, 0 is a lower bound.

What does "a.s." stand for? Is it a common usage?
My guess is "asymptotically" but I'd like to verify. 
 A: It stands for "almost surely," i.e. the probability of this occurring is 1.
See: https://en.wikipedia.org/wiki/Almost_surely
A: As mentioned above, a. s. stands for almost shurely, but in this case they are talking about almost shurely convergence. From the Wikipedia, 

To say that the sequence $X_n$ converges almost surely or almost everywhere or with probability 1 or strongly towards $X$ means that
  $$Pr(\lim_{n\to\infty}{X_n}=X)=1$$

A: As noted by @Matt, a.s. stands for "almost surely", or with probability 1. 
Why the "almost" in "almost surely"? Because just because something  happens "almost surely" does not mean it must happen. For example, suppose $X \sim$ Uniform(0,1). What's $P(X = 0.5)$? Well, since $X$ is a continuous random variable, $P(X = $ any finite set of values) = 0. Therefore, $X$ is almost surely not equal to 0.5. But that's not to say $X$ cannot be equal to 0.5! 
A: As already noted by others, "a.s." stands for "almost surely". The wikipedia article quoted by @Matt is a good start for almost surely and its synonyms.
There is however a subtle distinction between almost surely (or with probability 1) to always [resp., between with probability zero to never]. 
Imagine an infinite series of i.i.d. random variables which are head a.s. (=with probability 1), tail with probability zero. It is possible in such an infinite series to have a finite number of tails although the probability for tail is 0, as the empirical distribution of the series remains 1-0 (only a finite number of instances out of infinitely many). On the other hand, when one says that the series is always head one means that not even a single tail occurs in the series.
