New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem
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 .
-  Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, no. 3, The Mathematical Society of Japan, 1956. MR 0097489
-  P. C. Shields, A simple, direct proof of Birkhoff's ergodic theorem, preprint.
-  A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968. MR 0236587
- P. R. Halmos, Lectures on ergodic theory, Japan Math. Soc., Kenkyusha Printing Co., Ltd., Tokyo, 1956. MR 0097489 (20:3958)
- P. C. Shields, A simple, direct proof of Birkhoff's ergodic theorem, preprint.
- A. Zygmund, Trigonometric series, 2nd ed., Vol. 1, Cambridge Univ. Press, Cambridge, 1968, pp. 29-33. MR 0236587 (38:4882)
Keywords: Maximal ergodic theorem, maximal functions, Hardy-Littlewood maximal function
Article copyright: © Copyright 1983 American Mathematical Society