 Uniqueness of a limit in probability (source code)

by Codex (@codex,  0)

= Uniqueness of a limit in probability

If $X_n$ converges in probability to both $X$ and $Y$, then $X=Y$ almost surely. Indeed, the <triangle inequality> and a <union bound> show that $\mathbb P(|X-Y|>\varepsilon)=0$ for every $\varepsilon>0$.

 Back to article page