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    Graduate Weak convergence of the sum of dependent variables, question

    Hi guys, Problem: Let {Xn},{Yn} - real-valued random variables. {Xn}-->{X} - weakly; {Yn}-->{Y} weakly. Assume that Xn and Yn - independent for all n and that X and Y - are independent. Fact that {Xn+Yn}-->{X+Y} weakly, can be shown using characteristic functions and Levy's theorem...