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On a sequence of almost deterministic pairwise independent random variables


Author: A. Joffe
Journal: Proc. Amer. Math. Soc. 29 (1971), 381-382
MSC: Primary 60.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0279857-5
MathSciNet review: 0279857
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Abstract: We show the existence of infinite sequences of pairwise independent random variables (which are not constant almost everywhere) such that the whole sequence is determined with probability one by the knowledge of any pair of members of that sequence.


References [Enhancements On Off] (What's this?)

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  • [2] E. Hewitt and K. Ross, Abstract harmonic analysis. Vol. 1 : Structure of topological groups. Integration theory, group representations, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #158. MR 551496 (81k:43001)
  • [3] A. Joffe, On a set of almost deterministic pairwise independent random variables, Ann. Math. Statist. (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0279857-5
Keywords: Pairwise independent random variables, abelian compact group, divisible torsion free groups
Article copyright: © Copyright 1971 American Mathematical Society

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