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:
“It is impossible that had Buonaparte descended from a race of vegetable feeders that he could have had either the inclination or the power to ascend the throne of the Bourbons.”
—Percy Bysshe Shelley (1792–1822)
“In the event of an oxygen shortage on airplanes, mothers of young children are always reminded to put on their own oxygen mask first, to better assist the children with theirs. The same tactic is necessary on terra firma. There’s no way of sustaining our children if we don’t first rescue ourselves. I don’t call that selfish behavior. I call it love.”
—Joyce Maynard (20th century)