A topological version of Slutsky’s theorem
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- by Paul Ressel PDF
- Proc. Amer. Math. Soc. 85 (1982), 272-274 Request permission
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
- Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
- Paul Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 (1977), no. 1, 69–78. MR 486384, DOI 10.7146/math.scand.a-11676 E. E. Slutsky, Über stochastische Asymptoten und Grenzwerte, Metron 5 (1925), 1-90.
- Flemming Topsøe, Topology and measure, Lecture Notes in Mathematics, Vol. 133, Springer-Verlag, Berlin-New York, 1970. MR 0422560, DOI 10.1007/BFb0069481
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 272-274
- MSC: Primary 60B05; Secondary 28C15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652456-6
- MathSciNet review: 652456