ABSTRACT In this paper, using spanning sets in mean metrics we construct a new definition of measure-theoretic pressure of ergodic measures over a topological dynamical system. And we establish a pressure version of Katok's entropy formula in the case of mean metrics. Furthermore, we also introduce a new definition of topological pressure by replacing the Bowen metrics with the corresponding mean metrics, and prove that the new topological pressure is equivalent to the classical topological pressure. Then the variational principle for the newly defined topological pressure is obtained.

中文翻译：

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平均度量中的测量理论压力和拓扑压力

摘要在本文中，我们在平均度量中使用生成集，我们构建了拓扑动力系统上遍历测度的测度理论压力的新定义。我们在平均度量的情况下建立了卡托克熵公式的压力版本。此外，我们还通过用相应的平均度量替换 Bowen 度量来引入拓扑压力的新定义，并证明新的拓扑压力等效于经典拓扑压力。然后得到新定义的拓扑压力的变分原理。