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This would probably look like a dumb question (akin to prove $2=1$ type). But I'd still like to know where the flaw lies. The question is regarding convergence in probability and almost sure convergence. We know the following: Suppose events $A_n \to A$, then $P(A_n) \to P(A)$ i.e $\lim P(A_n) = P(\lim A_n) = P(A)$.

Can't the same principle be used to conclude equivalence of both type of convergence?

$P(\lim X_n = X) = \lim P(X_n = X)$, implying equivalence? Thanks!

Best,

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    For some basic information about writing math at this site see e.g. [here](http://meta.math.stackexchange.com/questions/5020/), [here](http://meta.stackexchange.com/a/70559/155238), [here](http://meta.math.stackexchange.com/questions/1773/) and [here](http://math.stackexchange.com/editing-help#latex).2012-10-30
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    Thanks for the edits!... sorry for being (extremely) sloppy at first!2012-10-30

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