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.


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

See: https://en.wikipedia.org/wiki/Almost_surely

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

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