PROBABILITIES Course

Almost sure convergence

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In French, it's Convergence presque sûre. The sequence $X_n$ converges almost surely if

@ \mathbb{P}(\lim_{n \to+ \infty} X_n = x) = 1 @

It's that's the case, then $x$ is a constant $c$ and the notation is

@ X_n \xrightarrow{a.s.} c @

This means that when $n\to+ \infty$ then almost surely $X_n \to c$.