Mathematics – Dynamical Systems
Scientific paper
2003-11-17
Mathematics
Dynamical Systems
14 pages
Scientific paper
Let $(X, \mathcal{B}, \mu)$ be a probability measure space and $T_1$, $T_2$, $T_3$ three not necessarily commuting measure preserving transformations on $(X, \mathcal{B}, \mu)$. 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.
No associations
LandOfFree
Pointwise convergence along cubes for measure preserving systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pointwise convergence along cubes for measure preserving systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pointwise convergence along cubes for measure preserving systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-605400