论文标题
$ \ bigoplus_ {p \ in p} \ mathbb {f} _p $ -Systems作为Abramov Systems
$\bigoplus_{p\in P}\mathbb{F}_p$-Systems as Abramov Systems
论文作者
论文摘要
令$ \ mathcal {p} $为（无界的）可计数的数量，让$ g = \ bigoplus_ {p \ in p} \ mathbb {f} _p $。我们研究了昂贵概率系统的$ k $'通用特征因素$（x，\ mathcal {b}，μ）$，相对于某种衡量$ g $的措施的操作。我们发现，这些因素的每个扩展是由多项式产生的，我们给出了一个不是阿布拉莫夫的ergodic $ g $系统的示例。特别是我们概括了伯格森·陶（Bergelson Tao）和齐格勒（Ziegler）的主要结果，他们在特殊情况下证明了类似的定理$ p = \ {p，p，p，p，... \} $，用于某些固定的prime $ p $。在随后的论文中，我们使用此结果证明了Ergodic $ \ bigoplus_ {p \ in P} \ Mathbb {f} _p $ -Systems的一般结构定理。
Let $\mathcal{P}$ be an (unbounded) countable multiset of primes, let $G=\bigoplus_{p\in P}\mathbb{F}_p$. We study the $k$'th universal characteristic factors of an ergodic probability system $(X,\mathcal{B},μ)$ with respect to some measure preserving action of $G$. We find conditions under which every extension of these factors is generated by phase polynomials and we give an example of an ergodic $G$-system that is not Abramov. In particular we generalize the main results of Bergelson Tao and Ziegler who proved a similar theorem in the special case $P=\{p,p,p,...\}$ for some fixed prime $p$. In a subsequent paper we use this result to prove a general structure theorem for ergodic $\bigoplus_{p\in P}\mathbb{F}_p$-systems.
