发表机构
Chongqing Jiaotong University; Chongqing University（重庆交通大学; 重庆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无限可数顺从群连续作用，引入近似乘积性质，证明其蕴含不变测度的熵稠密性与几乎熵可逼近性，并在渐近熵扩张条件下提升为熵可逼近性，进而实现中间熵遍历测度的完全实现。
AI 中文摘要
我们研究无限可数顺从群的连续作用的熵实现问题。我们为顺从群作用引入了一种近似乘积性质，该性质允许在预先指定的两两不相交、充分不变的有限集上出现小比例的追踪错误。我们证明该性质蕴含每个不变测度的熵稠密性和几乎熵可逼近性。该构造将零熵精确铺砌与追踪错误复杂性的有限块估计相结合。在渐近熵扩张性条件下，几乎熵可逼近性提升为熵可逼近性。对于每个$0\leq\alpha<h(X,G)$，熵为$\alpha$的遍历测度构成熵至少为$\alpha$的不变测度中的剩余子集。特别地，遍历测度熵的集合等于$[0,h(X,G)]$。
英文摘要
We study entropy realization for continuous actions of infinite countable amenable groups. We introduce an approximate product property for amenable group actions that permits a small proportion of tracing mistakes on prescribed pairwise disjoint, sufficiently invariant finite sets. We prove that this property implies entropy-denseness and almost entropy-approximability of every invariant measure. The construction combines zero-entropy exact tilings with a finite-block estimate for the complexity of tracing mistakes. Under asymptotic entropy expansiveness, almost entropy-approximability upgrades to entropy-approximability. For every $0\leqα<h(X,G)$, ergodic measures of entropy $α$ then form a residual subset of the invariant measures whose entropy is at least $α$. In particular, the set of ergodic measure entropies equals $[0,h(X,G)]$.37A35, 37B40, 37B05
