Extensions of Skorohod's almost sure representation Theorem

A well known result in probability is that convergence almost surely (a.s.) of a sequence of random elements implies weak convergence of their laws. The Ukrainian mathematician Anatoliy Volodymyrovych Skorohod proved the lemma known as Skorohod's a.s. representation Theorem, a partial converse of this result.;In Chapter 3 we present Cortissoz's result [5], a variant of Skorokhod's Theorem. It is shown that given a continuous path in M (S) it can be associated a continuous path with fixed endpoints in the space of S-valued random elements on a nonatomic probability space, endowed with the topology of convergence in probability.;In Chapter 4 we modify Blackwell and Dubins representation for particular cases of S, such as certain subsets of R or Rn.;In this work we discuss the notion of continuous representations, which allows us to provide generalizations of Skorohod's Theorem. In Chapter 2, we explore Blackwell and Dubins's extension [3] and Fernique's extension [10].