Almost Surely - Formal Definition

Formal Definition

Let (Ω, F, P) be a probability space. One says that an event E in F happens almost surely if P(E) = 1. Equivalently, we can say an event E happens almost surely if the probability of E not occurring is zero.

An alternative definition from a measure theoretic-perspective is that (since P is a measure over Ω) E happens almost surely if E = Ω almost everywhere.

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