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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A topological version of Slutsky's theorem


Author: Paul Ressel
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
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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.


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