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:
“The pretty fellows you speak of, I own entertain me sometimes, but is it impossible to be diverted with what one despises? I can laugh at a puppet show, at the same time I know there is nothing in it worth my attention or regard.”
—Mary Wortley, Lady Montagu (1689–1762)
“In each event of life, how clear
Thy ruling hand I see!
Each blessing to my soul more dear,
Because conferred by Thee.”
—Helen Maria Williams (18th century)