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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
MathSciNet review: 687641
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Abstract | References | Similar Articles | Additional Information

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] Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, no. 3, The Mathematical Society of Japan, 1956. MR 0097489 (20 #3958)
  • [2] P. C. Shields, A simple, direct proof of Birkhoff's ergodic theorem, preprint.
  • [3] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London, 1968. MR 0236587 (38 #4882)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687641-1
PII: S 0002-9939(1983)0687641-1
Keywords: Maximal ergodic theorem, maximal functions, Hardy-Littlewood maximal function
Article copyright: © Copyright 1983 American Mathematical Society