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A simple proof of some ergodic theorems

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Abstract

Some ideas of T. Kamae’s proof using nonstandard analysis are employed to give a simple proof of Birkhoff’s theorem in a classical setting as well as Kingman’s subadditive ergodic theorem.

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References

  1. T. Kamae,A simple proof of the ergodic theorem using nonstandard analysis, Isr. J. Math.42 (1982), 284–290.

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  2. J. F. C. Kingman,Subadditive ergodic theory, Ann. Probab.1 (1973), 883–909.

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Authors and Affiliations

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

    Yitzhak Katznelson & Benjamin Weiss

Authors
  1. Yitzhak Katznelson
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  2. Benjamin Weiss
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Katznelson, Y., Weiss, B. A simple proof of some ergodic theorems. Israel J. Math. 42, 291–296 (1982). https://doi.org/10.1007/BF02761409

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  • DOI: https://doi.org/10.1007/BF02761409

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