Pointwise convergence along cubes for measure preserving systems

Idris Assani

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Pointwise convergence along cubes for measure preserving systems

Idris Assani

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Abstract

Let $(X, \mathcal{B}, μ)$ be a probability measure space and $T_1$, $T_2$, $T_3$ three not necessarily commuting measure preserving transformations on $(X, \mathcal{B}, μ)$. We prove that for all bounded functions $f_1$, $f_2$, $f_3$ the averages $$\frac{1}{N^2}\sum_{n, m =1}^N f_1(T_1^nx)f_2(T_2^mx)f_3(T_3^{n+m}x)$$ converges a.e. Generalizations to averages of $2^k -1$ functions are also given for not necessarily commuting weakly mixing systems.

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BibTeX RIS

Idris Assani. 2003-11-17. Pointwise convergence along cubes for measure preserving systems. https://arxiv.org/abs/math/0311274

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