论文标题
相对熵的相对熵尺寸
Relative entropy dimensions for amenable group actions
论文作者
论文摘要
我们研究了可计数剂木材的相对熵零扩展的相对熵零扩展的拓扑复杂性。首先，对于给定的folner序列$ \ {f_n \} _ {n = 0}^\ infty $，我们分别定义了相对熵生成集的相对熵尺寸和相对拓扑相对相对拓扑复杂性的亚表达生长的尺寸。同时，我们研究了他们之间的关系。其次，我们介绍了相对维度集的概念。此外，使用它，我们讨论了相对熵零扩展之间的差异，该扩展概括了Dou，Huang和Park的结果[Trans。阿米尔。数学。 Soc。 363（2）（2011），659-680]。
We study the topological complexities of relative entropy zero extensions acted by countableinfinite amenable groups. Firstly, for a given Folner sequence $\{F_n\}_{n=0}^\infty$, we define respectively the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. Meanwhile, we investigate the relations among them. Secondly, we introduce the notion of a relative dimension set. Moreover, using it, we discuss the disjointness between the relative entropy zero extensions which generalizes the results of Dou, Huang and Park[Trans. Amer. Math. Soc. 363(2) (2011), 659-680].
