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Ergodic theorems for random sets with density zero
Published online by Cambridge University Press: 19 September 2008
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.
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- Copyright © Cambridge University Press 1994