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

Full-text PDF

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]**Paul R. Halmos,*Lectures on ergodic theory*, Publications of the Mathematical Society of Japan, no. 3, The Mathematical Society of Japan, 1956. MR**0097489****[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-New York, 1968. MR**0236587**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
28D05,
42B25,
47A35

Retrieve articles in all journals with MSC: 28D05, 42B25, 47A35

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