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On the existence of probability measures with given marginals

David Alan Edwards — 1978

Annales de l'institut Fourier

Let X be a compact ordered space and let μ , ν be two probabilities on X such that μ ( f ) ν ( f ) for every increasing continuous function f : X R . Then we show that there exists a probability θ on X × X such that (i) θ ( R ) = 1 , where R is the graph of the order in X , (ii) the projections of θ onto X are μ and ν . This theorem is generalized to the completely regular ordered spaces of Nachbin and also to certain infinite products. We show how these theorems are related to certain results of Nachbin,...

A Weierstrass-Stone theorem for Choquet simplexes

David Alan EdwardsG. F. Vincent-Smith — 1968

Annales de l'institut Fourier

Soit X un convexe compact d’un espace localement convexe séparé, soit A ( X ) l’espace de fonctions réelles affines continues sur X , et soit L un sous-espace de A ( X ) linéaire qui contient les fonctions constantes. Parmi les faces fermées de X sur lesquelles les fonctions de L sont toutes constantes on appelle les faces maximales L -faces. Nos théorèmes principaux donnent quelques conditions sous lesquelles L contient exactement ces fonctions qui sont constantes sur chaque L -face. En particulier, L est dense...

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