Almost surely  

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Given enough time, a chimpanzee punching at random on a typewriter would almost surely type out all of Shakespeare's plays.  Photo: Chimpanzee Typing (1907) - New York Zoological Society
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Given enough time, a chimpanzee punching at random on a typewriter would almost surely type out all of Shakespeare's plays.
Photo: Chimpanzee Typing (1907) - New York Zoological Society

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Train wreck at Montparnasse (October 22, 1895) by Studio Lévy and Sons.
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Train wreck at Montparnasse (October 22, 1895) by Studio Lévy and Sons.

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.

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Unless indicated otherwise, the text in this article is either based on Wikipedia article "Almost surely" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on original research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

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