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New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem


Author: Roger L. Jones
Journal: Proc. Amer. Math. Soc. 87 (1983), 681-684
MSC: Primary 28D05; Secondary 42B25, 47A35
DOI: https://doi.org/10.1090/S0002-9939-1983-0687641-1
MathSciNet review: 687641
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Abstract: A new proof of the maximal ergodic theorem is presented. The same idea used in this proof is then used to show that the Hardy-Littlewood maximal function is weak type $ (1,1)$.


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

  • [1] P. R. Halmos, Lectures on ergodic theory, Japan Math. Soc., Kenkyusha Printing Co., Ltd., Tokyo, 1956. MR 0097489 (20:3958)
  • [2] P. C. Shields, A simple, direct proof of Birkhoff's ergodic theorem, preprint.
  • [3] A. Zygmund, Trigonometric series, 2nd ed., Vol. 1, Cambridge Univ. Press, Cambridge, 1968, pp. 29-33. MR 0236587 (38:4882)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0687641-1
Keywords: Maximal ergodic theorem, maximal functions, Hardy-Littlewood maximal function
Article copyright: © Copyright 1983 American Mathematical Society

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