We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving (p.m.p.) actions of countablegroups introduced in Part I [B. Seward. Krieger’s finite generator theorem for actions of countable groups I. Invent. Math. 215(1) (2019), 265–310]. In this paper we prove a non-ergodic finite generator theorem and use it to establish sub-additivity and semicontinuity properties of Rokhlin entropy. We also obtain formulas for Rokhlin entropy in terms of ergodic decompositions and inverse limits. Finally, we clarify the relationship between Rokhlin entropy, sofic entropy, and classical Kolmogorov–Sinai entropy. In particular, using Rokhlin entropy we give a new proof of the fact that ergodic actions with positive sofic entropy have finite stabilizers.

中文翻译：

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可数群作用的 Krieger 有限生成器定理 III

我们继续研究 Rokhlin 熵，这是第一部分 [B. 苏厄德。可数群作用的 Krieger 有限生成器定理 I.发明。数学.215(1) (2019), 265–310]。在本文中，我们证明了一个非遍历有限生成器定理，并用它来建立 Rokhlin 熵的次可加性和半连续性。我们还根据遍历分解和逆限制获得了 Rokhlin 熵的公式。最后，我们阐明了 Rokhlin 熵、sofic 熵和经典 Kolmogorov-Sinai 熵之间的关系。特别是，使用 Rokhlin 熵，我们提供了一个新的证据，证明具有正 sofic 熵的遍历动作具有有限稳定器。