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 non-singular infinite direct products T of transformations $T_n$ , $n\in \mathbb N$ , of finite type is studied. It is shown that if $T_n$ is mildly mixing, $n\in \mathbb N$ , the sequence of 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 technique provides a new approach to the non-singular Gaussian transformations studied recently by Arano, Isono and Marrakchi.

证明了温和混合高斯变换上的每个高斯余环要么是高斯共边，要么是极弱混合。研究了有限类型的变换 $T_n$ , $n\in \mathbb N$ 的非奇异无限直积T类。结果表明，如果 $T_n$ 是温和混合的， $n\in \mathbb N$ ， $T_n$ 的 Radon-Nikodym 导数序列是渐近平移拟不变的并且T是保守的，那么T的 Maharam 扩展是急剧的弱混合。该技术为 Arano、Isono 和 Marrakchi 最近研究的非奇异高斯变换提供了一种新方法。