Journal of Symbolic Logic 47 (3):605 - 624 (1982)
|Abstract||We show that every formula of L ω 1p is equivalent to one which is a propositional combination of formulas with only one quantifier. It follows that the complete theory of a probability model is determined by the distribution of a family of random variables induced by the model. We characterize the class of distribution which can arise in such a way. We use these results together with a form of de Finetti's theorem to prove an almost sure interpolation theorem for L ω 1p|
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