Hello,

I'm needing some help here, please. Suppose that

weakly, where both measures are defined in , and that is the marginal of .

By Portmanteau's theorem, we have

for all A open. So far, ok. The problem arises now. I've been told that all the above implies

Can someone help me to prove that statement?

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The real problem is the following:

If

weakly, and if

and are the marginals of ,

the limit must have the same marginals.

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Thank you very much and happy new year!