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May 12, 2021 at 22:41 history edited G. Panel CC BY-SA 4.0
added 65 characters in body
May 12, 2021 at 20:38 comment added Dieter Kadelka In this form your question does not make sense. It should be: Does there exist a probability space and r.v. $X_n'$, $Y'$ on it such that the $X_n'$ have the same distribution as the $X_n$, $Y'$ the same distribution as $Y$ and with $f(X_n') \to Y'$ a.s.
May 12, 2021 at 18:07 comment added Jochen Wengenroth I don't understand the question. Either the random variables are given or to be constructed.
May 12, 2021 at 15:43 history asked G. Panel CC BY-SA 4.0