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Answer by Thomas Kojar for Can convergence in distribution necessarily be...
Skorokhod's representation theorem gives representation $X_{n}\to X$ of almost sure convergence and here is a proof for it.
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Let $X$ be a Polish space. Let $(\mu_n)_{n \in \mathbb{N} \cup \{\infty\}}$ be a family of Borel probability measures $\mu_n$ on $X$ such that $\mu_n \to \mu_\infty$ weakly as $n \to \infty$. For each...
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