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Given a squence of sets $\{S_{n}\}_{n=1}^{\infty}$, where each $S_{n}$ is countable set. I came over this statement in some article, it says: "Let $S$ be the weak limit of $S_{n}$". But I couldn't find a good definition for weak limit of a sequence of sets.

Any one know anything about this!

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    Could you possible add the source from which you got that?2012-06-04
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    Sorry, I just got some notes and didn't save that article. But you can consider it as a general question about weak convergence!2012-06-04
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    Is the question then "how would you define something called the weak limit of a sequence of sets"? Well, I'm going to define it to be $\varnothing$.2012-06-04

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