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Ergodic theorems for random sets with density zero

Published online by Cambridge University Press:  19 September 2008

Yenkun Huang
Yenkun Huang
Affiliation:
Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan, Republic of China
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Abstract

We generalize a result of Bourgain and a result of Huang. We also give a positive solution to A. Bellow's question: the a.e. convergence of the averages for σn = 1/n. On the other hand, we establish a sufficient and necessary condition for random sets in Z+ with asymptotic density zero which almost surely satisfy a mean ergodic theorem.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 1 , March 1994 , pp. 141 - 149
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

[1]Bellow, A. & Losert, V.. On sequences of density zero in ergodic theory. Contemp. Math. 26 (1984), 49–60.CrossRefGoogle Scholar
[2]Bourgain, J.. On the maximal ergodic theorem for certain subsets of integers. Isr. J. Math. 61 (1988), 39–72.CrossRefGoogle Scholar
[3]Chung, Kai Lai. A Course In Probability Theory Second Edition. Academic Press: New York, 1974.Google Scholar
[4]Huang, Yenkun. Random sets for the pointwise ergodic theorem. Ergod. Th. & Dynam. Sys. 12 (1992), 85–94.CrossRefGoogle Scholar