论文标题
在不相交系统的多个复发属性上
On the multiple recurrence properties for disjoint systems
论文作者
论文摘要
我们考虑在概率空间$（X，\ Mathcal {b}，μ）上，考虑互机的度量保存转换$ t_1，\ cdots，t_k $。我们获得了$ t_1，\ cdots，t_k $的多重复发属性，并且该结果可用于在公制空间中得出庞加莱类型的多次复发。我们还介绍了Khintchine类型的多重复发属性。此外，我们研究了多个不相交系统的多个沿着平均值，我们表明$ t_1，\ cdots，t_k $如果每个$ t_i $都是ergodic，则均匀地共同共同godic。
We consider mutually disjoint family of measure preserving transformations $T_1, \cdots, T_k$ on a probability space $(X, \mathcal{B}, μ)$. We obtain the multiple recurrence property of $T_1, \cdots, T_k$ and this result is utilized to derive multiple recurrence of Poincaré type in metric spaces. We also present multiple recurrence property of Khintchine type. Further, we study multiple ergodic averages of disjoint systems and we show that $T_1, \cdots, T_k$ are uniformly jointly ergodic if each $T_i$ is ergodic.
