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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] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
  • [2] Paul Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 (1977), no. 1, 69–78. MR 0486384
  • [3] E. E. Slutsky, Über stochastische Asymptoten und Grenzwerte, Metron 5 (1925), 1-90.
  • [4] Flemming Topsøe, Topology and measure, Lecture Notes in Mathematics, Vol. 133, Springer-Verlag, Berlin-New York, 1970. MR 0422560

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DOI: https://doi.org/10.1090/S0002-9939-1982-0652456-6
Article copyright: © Copyright 1982 American Mathematical Society