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Mathematical Research Letters
Volume 16 (2009)
Number 5
An $L^1$ ergodic theorem for sparse random subsequences
Pages: 849 – 859
DOI: https://dx.doi.org/10.4310/MRL.2009.v16.n5.a8
Author
Abstract
We prove an $L^1$ subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of universally $L^1$-good sequences nearly as sparse as the set of squares. In the process, we prove that a certain deterministic condition implies a weak maximal inequality for a sequence of $ℓ^1$ convolution operators (Prop. 3.1).
Published 1 January 2009