On a sequence of almost deterministic pairwise independent random variables
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.
-  Paul R. Halmos and John von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2) 43 (1942), 332–350. MR 0006617, https://doi.org/10.2307/1968872
-  Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
-  A. Joffe, On a set of almost deterministic pairwise independent random variables, Ann. Math. Statist. (to appear).
- P. Halmos and J. von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2) 43 (1942), 332-350. MR 4, 14. MR 0006617 (4:14e)
- 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)
- A. Joffe, On a set of almost deterministic pairwise independent random variables, Ann. Math. Statist. (to appear).
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Keywords: Pairwise independent random variables, abelian compact group, divisible torsion free groups
Article copyright: © Copyright 1971 American Mathematical Society