I think it does, I've tried proving it by using Chebishev's Inequality but it only prove that it works with quadratic convergence and I can't adapt it... Can you help me please? Thank you very much!
SOLVED
2026-03-26 09:40:24.1774518024
Does $E(|X_n - X|) \rightarrow 0$ implies $X_n$ converges in probability to $X$?
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$$P(|X_n-X|\geqslant\varepsilon)\leqslant\varepsilon^{-1}E(|X_n-X|)$$