Formal Definition
Let be a probability space. An event happens almost surely if . Equivalently, happens almost surely if the probability of not occurring is zero: . More generally, any event (not necessarily in ) happens almost surely if is contained in a null set: a subset of some such that . The notion of almost sureness depends on the probability measure . If it is necessary to emphasize this dependence, it is customary to say that the event occurs -almost surely or almost surely .
Read more about this topic: Impossible Event
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