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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the concentration and extension of cylinder measures

Author: Alejandro D. de Acosta
Journal: Trans. Amer. Math. Soc. 160 (1971), 217-228
MSC: Primary 28.46; Secondary 60.00
MathSciNet review: 0283168
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Abstract: It is shown that with respect to certain set-theoretic operations-- directed decreasing or even arbitrary intersections of certain families of convex, balanced, weakly closed sets--cylinder measures behave almost as regular Borel measures do. A refinement is proved when the cylinder measure satisfies a scalar concentration condition. These results are applied to obtain stronger versions of Prohorov's theorem and an extension theorem for complete Hausdorff locally convex spaces generalizing a result of Dudley, Feldman, and Le Cam.

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Keywords: Cylinder measure, concentration up to $ \varepsilon $, scalar concentration, Prohorov's extension theorem, extension of cylinder measures in complete spaces
Article copyright: © Copyright 1971 American Mathematical Society

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