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Weakly mixing PET

Published online by Cambridge University Press:  19 September 2008

V. Bergelson
V. Bergelson
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, USA
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Suppose that (X, ℬ, μ) is a probability measure space and T is an invertible measure perserving transformation of (X, ℬ, μ). T is called weakly mixing if for any two sets A1A2 ∈ ℬ one has:

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 3 , September 1987 , pp. 337 - 349
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[F1]Furstenberg, H.. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. d'Analyse Math. 31 (1977), 204–256.CrossRefGoogle Scholar
[F2]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton, New Jersey, 1981.CrossRefGoogle Scholar
[F3]Furstenberg, H.. IP-systems in ergodic theory. Contemporary Mathematics 26 (1984), 131–148.CrossRefGoogle Scholar
[FK1]Furstenberg, H. & Katznelson, Y.. An ergodic Szemerédi theorem for commuting transformations. J. d'Analyse Math. 34 (1978), 275–291.CrossRefGoogle Scholar
[FK2]Furstenberg, H. & Katznelson, Y.. An ergodic Szemerédi theorem for IP-systems and combinatorial theory. To appear in J. d'Analyse Math.Google Scholar
[FKO]Furstenberg, H., Katznelson, Y. & Ornstein, D.. The ergodic theoretical proof of Szemerédi's theorem. Bull. Amer. Math. Soc. 7 (1982), 527–552.CrossRefGoogle Scholar
[FW]Furstenberg, H. & Weiss, . The finite multipliers of infinite ergodic transformations. In Structure of Attractors in Dynamical Systems, Springer Lecture Notes #668, Springer (1978), 127–133.CrossRefGoogle Scholar
[KN]Kuipers, L. & Niederreiter, H.. Uniform Distribution of Sequences. Wiley, New York, 1974.Google Scholar