In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal equicontinuous factor. This result is obtained as an application of a general criterion which states that if a minimal system under an amenable group action is an almost finite to one extension of its maximal equicontinuous factor and has no infinite independent sets of length k for some $k\ge 2$, then it has only finitely many ergodic measures.

中文翻译：

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最少有遍历量度的最小系统

在本文中，证明了如果最小系统具有其序列熵对于所有序列均匀有界的性质，则它仅具有有限的遍历量，并且对于其最大等连续因子的一个扩展几乎是有限的。该结果是通过应用通用准则而得出的，该准则指出，如果在可接受的群作用下的最小系统对其最大等连续因子的一个扩展几乎是有限的，并且对于某些变量，则没有无限独立的长度k集$ķ\ge \mathrm{2个}$，那么它只有有限的遍历测度。