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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convergence of sequences of pairwise independent random variables


Authors: N. Etemadi and A. Lenzhen
Journal: Proc. Amer. Math. Soc. 132 (2004), 1201-1202
MSC (2000): Primary 60F15
Published electronically: September 11, 2003
MathSciNet review: 2045438
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Abstract: In spite of the fact that the tail $\sigma$-algebra of a sequence of pairwise independent random variables may not be trivial, we have discovered that if such a sequence converges in probability or almost everywhere, then the limit has to be a constant. This enables us to provide necessary and sufficient conditions for its convergence, in terms of its marginal distribution functions.


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Additional Information

N. Etemadi
Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), 322 Science and Engineering Offices, 851 South Morgan Street, Chicago, Illinois 60607-7045
Email: etemadi@uic.edu

A. Lenzhen
Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), 322 Science and Engineering Offices, 851 South Morgan Street, Chicago, Illinois 60607-7045
Email: lenzhen@math.uic.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07236-8
PII: S 0002-9939(03)07236-8
Keywords: Limit theorems, pairwise independence
Received by editor(s): September 26, 2002
Received by editor(s) in revised form: November 18, 2002
Published electronically: September 11, 2003
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2003 American Mathematical Society