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A topological version of Slutsky's theorem

Author: Paul Ressel
Journal: Proc. Amer. Math. Soc. 85 (1982), 272-274
MSC: Primary 60B05; Secondary 28C15
MathSciNet review: 652456
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Abstract: For weak convergence of probability measures on a product of two topological spaces the convergence of the marginals is certainly necessary. If however the marginals on one of the factor spaces converge to a one-point measure, the condition becomes sufficient, too. This generalizes a well-known result of Slutsky.

References [Enhancements On Off] (What's this?)

  • [1] P. Billingsley, Convergence of probability measures, Wiley, New York, 1968. MR 0233396 (38:1718)
  • [2] P. Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 (1977), 69-78. MR 0486384 (58:6130)
  • [3] E. E. Slutsky, Über stochastische Asymptoten und Grenzwerte, Metron 5 (1925), 1-90.
  • [4] F. Topsøe, Topology and measure, Lecture Notes in Math., vol. 133, Springer-Verlag, Berlin and New York, 1970. MR 0422560 (54:10546)

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Article copyright: © Copyright 1982 American Mathematical Society

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