ABSTRACT We present a simple proof of the fairly general fact that an invariant right-weak Gibbs probability measure is an equilibrium state, using a generalization of the formula of Brin and Katok for the local metric entropy. This new formula also allows us to clarify the role of the topological pressure on the standard definition of the Gibbs property.

中文翻译：

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弱吉布斯测度和均衡状态

摘要 我们使用 Brin 和 Katok 公式对局部度量熵的推广，提出了一个相当普遍的事实的简单证明，即不变的右弱 Gibbs 概率测度是一种平衡状态。这个新公式还使我们能够阐明拓扑压力对吉布斯性质的标准定义的作用。