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arXiv · 1406.2608

On the pointwise convergence of multiple ergodic averages

E. H. El Abdalaoui
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Abstract

It is shown that there exist a subsequence for which the multiple ergodic averages of commuting invertible measure preserving transformations of a Lebesgue probability space converge almost everywhere provided that the maps are weakly mixing with an ergodic extra condition. The proof provides a example of non-singular dynamical system for which the maximal ergodic inequality does not hold. We further get that the non-singular strategy to solve the pointwise convergence of the Furstenberg ergodic averages fails.

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E. H. El Abdalaoui. 2014-06-10. On the pointwise convergence of multiple ergodic averages. https://arxiv.org/abs/1406.2608

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