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Does anybody know a good reference for properties of convergence of random variables?

For example, if $X_n$ converges almost surely (a.s) to $X$ and if $Y_n$ converges a.s to $Y$, then $X_n Y_n$ converges a.s. to $XY$?

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You can have a look at Grimmet (Probability and Random processes from Oxford). It is very complete and has a chapter on Convergence of Random Variables (Chapter 7 in the third edition). You'll find many useful properties. However the property you gave as an example is a bit "basic"; you should be comfortable proving this before delving further into more advanced notions of convergence. When properties are that simple, applying the definition works most of the time in the proof.

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  • $\begingroup$ That property was just an example. However, since I want to use it, I don't want to prove it and waste some space and time. So, I felt like I can use it by citing a book, or paper. Is that also available there? $\endgroup$ – Susan_Math123 Jul 9 '16 at 22:35
  • $\begingroup$ Do you have a link for the pdf? $\endgroup$ – Susan_Math123 Jul 9 '16 at 22:43

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