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Media type:
E-Article
Title:
An extension of Skorohod’s almost sure representation theorem
Contributor:
Blackwell, David;
Dubins, Lester E.
Published:
American Mathematical Society (AMS), 1983
Published in:
Proceedings of the American Mathematical Society, 89 (1983) 4, Seite 691-692
Language:
English
DOI:
10.1090/s0002-9939-1983-0718998-0
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
Skorohod discovered that if a sequence Q n {Q_n} of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are Q n {Q_n} -distributed f n {f_n} which converge almost surely. This note strengthens Skorohod’s result by associating, with each probability Q Q on a Polish space, a random variable f Q {f_Q} on a fixed standard probability space so that for each Q Q , (a) f Q {f_Q} has distribution Q Q and (b) with probability 1, f P {f_P} is continuous at P = Q P = Q .