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:
“Do you still believe it impossible we exist? You didn’t actually think you were the only inhabited planet in the universe. How can any race be so stupid?”
—Edward D. Wood, Jr. (1922–1978)
“When we awoke, we found a heavy dew on our blankets. I lay awake very early, and listened to the clear, shrill ah, te te, te te, te of the white-throated sparrow, repeated at short intervals, without the least variation, for half an hour, as if it could not enough express its happiness. Whether my companions heard it or not, I know not, but it was a kind of matins to me, and the event of the forenoon.”
—Henry David Thoreau (1817–1862)