Baby Skorohod Theorem
# Statement
Let be a Sequence of Random Variables (not necessarily defined on the same Probability Space
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) so that . Then there exist {X^{#}_{n} : n \geq 0 } defined on Probability SpaceProbability Space
(where is the Lebesgue Measure) so thatProbability Space
\begin{align*} &X_{n}^{#} \overset{d}= X_{n} \text{ for } n \geq 0\\ &X_{n}^{#} \to X_{0}^{#} \text{ a.s.}\\ \end{align*}