On the concentration and extension of cylinder measures

de Acosta, Alejandro D.

doi:10.1090/S0002-9947-1971-0283168-6

On the concentration and extension of cylinder measures
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by Alejandro D. de Acosta

Trans. Amer. Math. Soc. 160 (1971), 217-228

DOI: https://doi.org/10.1090/S0002-9947-1971-0283168-6

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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.

References

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