Abstract
In this paper we present a variant of the well-known Skorokhod Representation Theorem. First we prove, given S S a Polish Space, that to a given continuous path α \alpha in the space of probability measures on S S , we can associate a continuous path in the space of S S -valued random variables on a nonatomic probability space (endowed with the topology of the convergence in probability). We call this associated path a lifting of α \alpha . An interesting feature of our result is that we can fix the endpoints of the lifting of α \alpha , as long as their distributions correspond to the respective endpoints of α \alpha . Finally, we also discuss and prove an n n -dimensional generalization of this result.
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