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Measurable recurrence and quasi-invariant measures

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Abstract

We characterize the wandering sets of a Borel automorphismT as being precisely those sets which have measure zero for every non-atomic measure μ which is quasi-invariant and ergodic forT.

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References

  1. Y. Katznelson and B. Weiss,The construction of quasi-invariant measures, Isr. J. Math.12 (1972), 1–4.

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  2. J. C. Oxtoby,Measure and Category, Springer, New York, 1971.

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  3. B. Weiss,Orbit equivalence of non-singular actions, inThéorie Ergodique, Monog. 29, L'Enseignement Math., 1981, pp. 77–107.

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Authors and Affiliations

  1. Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah & Benjamin Weiss

Authors
  1. Saharon Shelah
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  2. Benjamin Weiss
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Shelah, S., Weiss, B. Measurable recurrence and quasi-invariant measures. Israel J. Math. 43, 154–160 (1982). https://doi.org/10.1007/BF02761726

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  • DOI: https://doi.org/10.1007/BF02761726

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