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arXiv:math/0305388 [math.DS]AbstractReferencesReviewsResources

Pointwise convergence of averages along cubes

Idris Assani

Published 2003-05-27, updated 2003-11-23Version 2

Let $(X,\mathcal{B},\mu, T)$ be a measure preserving system. We prove the pointwise convergence of the averages $$\frac{1}{N^2}\sum_{n,m= 0}^{N-1} f_1(T^nx)f_2(T^mx)f_3(T^{n+m}x)$$ and of similar averages with seven bounded functions.

Comments: 18 pages, latex, We have replaced Lemma 2 with a new one. We also have added a reference
Categories: math.DS
Subjects: 37A30
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