Averages along cubes for not necessarily commuting measure preserving transformations

Idris Assani

paper

Averages along cubes for not necessarily commuting measure preserving transformations

arXiv:math/0511062

Abstract

We study the pointwise convergence of some weighted averages linked to averages along cubes. We show that if $(X, B, μ, T_{i})$ are not necessarily commuting measure preserving systems on the same finite measure space and if $f_{i},$ $1 \leq i \leq 6$ are bounded functions then the averages $\frac{1}{N ^{3}} n, m, p = 1 \sum N f_{1} (T_{1}^{n} x) f_{2} (T_{2}^{m} x) f_{3} (T_{3}^{p} x) f_{4} (T_{4}^{n + m} x) f_{5} (T_{5}^{n + p} x) f_{6} (T_{6}^{m + p} x)$ converge almost everywhere.

28 pages

Cited by in corpus (1)

Note sur la continuité de la projection dans les facteurs de Host-Kra