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.

**Answer**

It stands for “almost surely,” i.e. the probability of this occurring is 1.

**Attribution***Source : Link , Question Author : HBat , Answer Author : Matt*