New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem
HTML articles powered by AMS MathViewer
- by Roger L. Jones
- Proc. Amer. Math. Soc. 87 (1983), 681-684
- DOI: https://doi.org/10.1090/S0002-9939-1983-0687641-1
- PDF | 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
Bibliographic 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