Strongly ergodic sequences of integers and the individual ergodic theorem

Authors:
J. R. Blum and J. I. Reich

Journal:
Proc. Amer. Math. Soc. **86** (1982), 591-595

MSC:
Primary 28D05; Secondary 47A35, 60F15

DOI:
https://doi.org/10.1090/S0002-9939-1982-0674086-2

MathSciNet review:
674086

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an increasing sequence of positive integers. We call *strongly ergodic* if for every measure preserving transformation on a probability space and every we have a.e. where is the appropriate limit guaranteed by the individual ergodic theorem. We give sufficient conditions for a sequence to be strongly ergodic and provide examples.

**[1]**J. R. Blum and B. Eisenberg,*Generalized summing sequences and the mean ergodic theorem*, Proc. Amer. Math. Soc.**42**(1974), 423-429. MR**0330412 (48:8749)****[2]**J. R. Blum and R. Cogburn,*On ergodic sequences of measures*, Proc. Amer. Math. Soc.**51**(1975), 359-365. MR**0372529 (51:8736)****[3]**W. R. Emerson,*The pointwise ergodic theorem for amenable groups*, Amer. J. Math.**96**(1974), 472-487. MR**0354926 (50:7403)****[4]**A. M. Garsia,*Topics in almost everywhere convergence*, Markham, Chicago, Ill., 1970. MR**0261253 (41:5869)****[5]**J. I. Reich,*On the individual ergodic theorem for subsequences*, Ann. Probability**5**(1977), 1039-1046. MR**0444906 (56:3252)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
28D05,
47A35,
60F15

Retrieve articles in all journals with MSC: 28D05, 47A35, 60F15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0674086-2

Keywords:
Individual ergodic theorems,
subsequences,
strongly ergodic sequences

Article copyright:
© Copyright 1982
American Mathematical Society