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Random sets for the pointwise ergodic theorem

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 devise more general criteria which guarantee that the corresponding random set in Z+ almost surely satisfies a pointwise ergodic theorem on Lp for p > 1. Several large classes of examples are constructed. We also show that under a simple condition the corresponding random set in Z+ almost surely satisfies a pointwise ergodic theorem not only on Lp for p > 1 but also on L1. On the other hand, we establish a criterion to conclude that a certain class of random sets have Banach density zero. In particular, all of the examples mentioned have Banach density zero.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 85 - 94
Copyright
Copyright © Cambridge University Press 1992

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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]Conze, J. P., Convergence des moyennes ergodiques pour des soussuites. Bull. Soc. Math. France 35 (1973), 7–15.Google Scholar
[4]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press: Princeton, 1981.CrossRefGoogle Scholar
[5]Garsia, A. M.. Topics in Almost Everywhere Convegence. Markham Chicago, I11., 1970.Google Scholar