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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem
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by Roger L. Jones PDF
Proc. Amer. Math. Soc. 87 (1983), 681-684 Request permission

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
  • Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, vol. 3, Mathematical Society of Japan, Tokyo, 1956. MR 0097489
    • P. C. Shields, A simple, direct proof of Birkhoff’s ergodic theorem, preprint.
  • A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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