报告题目: Pointwise convergence of multiple ergodic averages and strictly ergodic models
报告人：  黄文教授   四川大学 中国科技大学  杰青获得者 
报告时间：2014年12月26日上午9:30-11:00
报告地点：数学楼二楼学术报告厅





摘要： 
By building some suitable strictly ergodic models, we prove that for an ergodic system $(X,mathcal{X},mu, T)$,  $dinmathbb{N}$, $f_1, ldots, f_d inL^{infty}(mu)$, the averages
begin{equation*}
    frac{1}{N^2} sum_{(n,m)in [0,N-1]^2}
    f_1(T^nx)f_2(T^{n+m}x)ldots f_d(T^{n+(d-1)m}x)
end{equation*}
converge $mu$ a.e.
 
Deriving some results from the construction, for distal systems we answer positively the question if the multiple ergodic averages converge a.e. That is, we show that if $(X,mathcal{X},mu, T)$ is an ergodic distal system, and $f_1, ldots, f_d in L^{infty}(mu)$, then multiple ergodic averages
begin{equation*}
    frac{1}{N}sum_{n=0}^{N-1}f_1(T^nx)ldots f_d(T^{dn}x)
end{equation*}
converge $mu$ a.e..