Impossible Event

Impossible Event

In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. The concept is analogous to the concept of "almost everywhere" in measure theory. While there is no difference between almost surely and surely (that is, entirely certain to happen) in many basic probability experiments, the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces. Basic examples of use include the law of large numbers (strong form) or continuity of Brownian paths.

Almost never describes the opposite of almost surely; an event which happens with probability zero happens almost never.

Read more about Impossible Event:  Formal Definition, "Almost Sure" Versus "sure", Asymptotically Almost Surely

Famous quotes containing the words impossible and/or event:

    “One can’t believe impossible things.”
    “I daresay you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    When little boys grown patient at last, weary,
    Surrender their eyes immeasurably to the night,
    The event will rage terrific as the sea;
    Their bodies fill a crumbling room with light.
    Allen Tate (1899–1979)