ABSTRACT Let be a flow, which means that X is a compact metric space and T is a group action on X and let , and be the sets of all nonempty compact subsets of X, all Borel probability measures on X and all upper semi-continuous fuzzy sets on X, respectively. Then , and are metric spaces under the Hausdorff metric, the prohorov metric and the level-wise metric, respectively. So the group T can naturally action on , and to generate new flows , and . The aim of this paper is to investigate the relation of transitivity and sensitivity among and , and . Actually it was proved that is weakly-mixing⇔ is transitive⇔ is weakly-mixing is weakly-mixing⇔ is transitive; is equicontionuous⇔ is equicontionuous⇔ is equicontionuous is distal ⇔ is equicontionuous ⇔ is distal; is -sensitive ⇔ is -sensitive ⇔ is -sensitive ⇔ is -sensitive, here is a filter of T.

中文翻译：

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关于群体行动的传递性和敏感性

摘要 设是一个流，这意味着 X 是一个紧度量空间，T 是 X 上的一个群动作，令 ，并且是 X 的所有非空紧致子集、X 上的所有 Borel 概率测度和所有上半连续的集合X 上的模糊集，分别。然后 ， 和 分别是 Hausdorff 度量、prohorov 度量和水平度量下的度量空间。所以组 T 可以自然地作用于，并产生新的流，和。本文的目的是研究和，和之间的传递性和敏感性的关系。实际上证明了弱混合⇔是传递性的⇔是弱混合性⇔是传递性的；是等距的⇔ 是等距的⇔ 是等距的，是远端的 ⇔ 是等距的 ⇔ 是远端的；is -sensitive ⇔ is -sensitive ⇔ is -sensitive ⇔ is -sensitive，这里是 T 的过滤器。