Weak convergences of probability measures: A uniform principle

Lasserre, Jean

doi:10.1090/S0002-9939-98-04390-1

Weak convergences of probability measures: A uniform principle
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by Jean B. Lasserre PDF

Proc. Amer. Math. Soc. 126 (1998), 3089-3096 Request permission

Abstract:

We consider a set $\prod$ of probability measures on a locally compact separable metric space. It is shown that a necessary and sufficient condition for (relative) sequential compactness of $\prod$ in various weak topologies (among which the vague, weak and setwise topologies) has the same simple form; i.e. a uniform principle has to hold in $\prod$. We also extend this uniform principle to some Köthe function spaces.

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