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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Weak convergences of probability measures:
A uniform principle

Author: Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 126 (1998), 3089-3096
MSC (1991): Primary 60B05, 60B10, 28A33
MathSciNet review: 1452809
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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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Additional Information

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse Cédex, France

Keywords: Sequences of measures, weak convergences of measures, Banach lattices, K\"{o}the function spaces
Received by editor(s): November 25, 1996
Received by editor(s) in revised form: March 10, 1997
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1998 American Mathematical Society