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Weak Convergences of Probability Measures: A Uniform Principle
Jean B. Lasserre
Proceedings of the American Mathematical Society
Vol. 126, No. 10 (Oct., 1998), pp. 3089-3096
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119115
Page Count: 8
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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.
Proceedings of the American Mathematical Society © 1998 American Mathematical Society