ABSTRACT In this paper, we formulate the notions of weighted upper metric mean dimensions and weighted upper measure-theoretic mean dimensions for amenable group actions. In particular, a variational principle for amenable group actions is presented. We also define weighted upper metric mean dimensions with respect to pseudo-orbits and establish their relation to weighted upper metric mean dimensions.

中文翻译：

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适合组操作的加权上限度量平均维度

摘要在本文中，我们制定了加权上度量平均维数和加权上度量理论平均维数的概念，以适应群体行为。特别是，提出了一个适用于群体行动的变分原则。我们还定义了关于伪轨道的加权上度量平均维度，并建立了它们与加权上度量平均维度的关系。