In probability theory, an event is said to happen almost surely, sometimes abbreviated a.s., if it happens with probability 1 with respect to the underlying probability measure. Equivalently, the set of outcomes on which the event fails to happen has probability zero, even though that set may still be non-empty. The distinction between an event that is certain and one that merely happens almost surely becomes meaningful in infinite sample spaces, where non-empty sets of probability zero genuinely exist.
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In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the probability measure).
In Branch: Probability and Statistics, Lead sentence
In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (
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