Pointwise convergence along cubes for measure preserving systems
| dc.creator | Assani, Idris | |
| dc.date | 2003-11-17 | |
| dc.date.accessioned | 2026-07-07T05:02:57Z | |
| dc.date.available | 2026-07-07T05:02:57Z | |
| dc.description | 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. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311274 | |
| dc.identifier | http://arxiv.org/abs/math/0311274 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69219 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A30 | |
| dc.title | Pointwise convergence along cubes for measure preserving systems | |
| dc.type | text |