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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0283168-6
PII: S 0002-9947(1971)0283168-6
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