Title: Random sets for the pointwise ergodic theorem
Abstract: 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 L p 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 L p for p > 1 but also on L 1 . 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.
Publication Year: 1992
Publication Date: 1992-03-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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