AI 中文总结
该研究针对拓扑混合有限型移位，证明了Ornstein的$\bar{d}$度量下最大熵测度的有效唯一性，强化了Kadyrov在Wasserstein度量下的相关结果。
AI 中文摘要
每一个拓扑混合的有限型移位都具有唯一的最大熵测度（MME）。根据Ornstein理论，每一个熵接近最大的不变测度在$\bar{d}$度量下必须接近该最大熵测度。我们证明了该结论的量化版本，强化了Kadyrov此前在Wasserstein度量下建立有效唯一性的结果。
英文摘要
Every topologically mixing shift of finite type has a unique measure of maximal entropy. It follows from Ornstein theory that every invariant measure with entropy close to maximal must be close to the MME in the $\bar{d}$-metric. We prove a quantitative version of this, strengthening earlier results of Kadyrov that established effective uniqueness in the Wasserstein metric.
Comments18 pages, 1 figure
