PROBABILITIES Course

Convergence in (quadratic/square) mean

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In French, it's Convergence en moyenne quadratique. The sequence $X_n$ converges in mean=quadratic mean=square mean if

@ \lim_{n \to+ \infty} \mathbb{E}((X_n-x)^2) = 0 @

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

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