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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convergence of sequences of pairwise independent random variables
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by N. Etemadi and A. Lenzhen PDF
Proc. Amer. Math. Soc. 132 (2004), 1201-1202 Request permission

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
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1201-1202
  • MSC (2000): Primary 60F15
  • DOI: https://doi.org/10.1090/S0002-9939-03-07236-8
  • MathSciNet review: 2045438