We extend the definition of topological entropy for any (not necessarily continuous) amenable groups acting on a compact space by defining entropy of arbitrary subsets of a product space. We investigate how this new notion of topological entropy for amenable group actions behaves and some of its basic properties; among them are the behavior of the entropy with respect to disjoint union, Cartesian product, and some continuity properties with respect to Vietoris topology. As a special case for \(1\leq p\leq \infty \), the Bowen p-entropy of sets is introduced. It is shown that the notions of generalized topological entropy and Bowen \(\infty \)-entropy for compact metric spaces coincide.

通过定义乘积空间的任意子集的熵，我们扩展了对作用于紧空间上的任何（不一定连续）顺应性组的拓扑熵的定义。我们研究了适用于群体行为的拓扑熵这一新概念的行为方式及其一些基本特性。其中包括熵关于不相交联合，笛卡尔乘积以及关于维耶托里斯拓扑的某些连续性的行为。作为\（1 \ leq p \ leq \ infty \）的特例，引入了集合的Bowen p熵。结果表明，紧凑度量空间的广义拓扑熵和Bowen \（\ infty \）-熵的概念是一致的。