Mathematical Research Letters
Volume 16 (2009)
An $L^1$ ergodic theorem for sparse random subsequences
Pages: 849 – 859
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).