|ISSN 1088-6826(online) ISSN 0002-9939(print)|
An extension of Skorohod's almost sure representation theorem
Abstract: Skorohod discovered that if a sequence of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are -distributed which converge almost surely. This note strengthens Skorohod's result by associating, with each probability on a Polish space, a random variable on a fixed standard probability space so that for each , (a) has distribution and (b) with probability 1, is continuous at .
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