不变测度的独立性、序列熵与均值敏感性
Independence, sequence entropy and mean sensitivity for invariant measures
AI总结：
本文研究了可数无限离散群作用下保测系统中独立性、序列熵与均值敏感性的联系，证明了序列熵元组均为IT元组，并在顺从群和遍历测度条件下证明了三类敏感元组的一致性。
摘要：
我们研究在可数无限离散群作用下，保测系统中独立性、序列熵与均值敏感性之间的联系。我们证明不变测度的每个序列熵元组都是IT元组。此外，若作用群是顺从群，我们证明对于遍历测度，序列熵元组、沿某缓和Følner序列的均值敏感元组与沿某缓和Følner序列的均值敏感性元组是一致的。
英文摘要：
We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group. We establish that every sequence entropy tuple for an invariant measure is an IT tuple. Furthermore, if the acting group is amenable, we show that for an ergodic measure, the sequence entropy tuples, the mean sensitive tuples along some tempered Følner sequence, and the sensitive in the mean tuples along some tempered Følner sequence coincide.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
