论文标题
IDPFT系统和非语音高斯动作的阵尾共生
Ergodic cocycles of IDPFT systems and nonsingular Gaussian actions
论文作者
论文摘要
事实证明，在轻度混合高斯转化上的每个高斯旋钮是高斯串联或急剧较弱的混合。研究了有限类型（IDPFT）的非单ingular无限直接产品$ t $转换$ t_n $，$ n \ in \ bbb n $。结果表明，如果$ t_n $是温和的混合，$ n \ in \ bbb n $，则$ t_n $的radon-nikodym衍生物的序列是渐近地翻译quasi-Invariant，而$ t $是保守的，那么$ t $的maharam扩展是$ t $的Maharam Extension。这种技术为Arano，Isono和Marrakchi最近研究的非语言高斯转换提供了一种新的方法。
It is proved that each Gaussian cocycle over a mildly mixing Gaussian transformation is either a Gaussian coboundary or sharply weak mixing. The class of nonsingular infinite direct products $T$ of transformations $T_n$, $n\in\Bbb N$, of finite type (IDPFT) is studied. It is shown that if $T_n$ is mildly mixing, $n\in\Bbb N$, the sequence of the Radon-Nikodym derivatives of $T_n$ is asymptotically translation quasi-invariant and $T$ is conservative then the Maharam extension of $T$ is sharply weak mixing. This techniques provides a new approach to the nonsingular Gaussian transformations studied recently by Arano, Isono and Marrakchi.
