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:
“I look on Sculpture as history. I do not think the Apollo and the Jove impossible in flesh and blood. Every trait the artist recorded in stone, he had seen in life, and better than his copy.”
—Ralph Waldo Emerson (1803–1882)
“This event advertises me that there is such a fact as death,—the possibility of a man’s dying. It seems as if no man had ever died in America before; for in order to die you must first have lived.”
—Henry David Thoreau (1817–1862)