论文标题
拓扑稳定和$β$ - 团体动作的观点
Topologically stable and $β$-persistent points of group actions
论文作者
论文摘要
在本文中，我们引入了拓扑稳定的积分，$β$ - 取消点，$β$ - 透明的财产，$β$ - 持久的度量和几乎$β$ - 首先可计数的紧凑型公制空间的Hausdorff组动作的措施。我们证明，所有$β$ - 垂直点的集合都是可以衡量的，如果该动作是公平的，则它是封闭的。我们还证明，所有$β$ compersist的措施的集合都是凸集，每几乎$β$ - 取消度量是$β$ - 近距离的度量。最后，我们证明，紧凑型公制空间的每一个均等均值稳定的首先可计数的Hausdorff组动作均为$β$ - 呈现。特别是，每一个均值的拓扑稳定流量为$β$ - 呈稳定性。
In this paper, we introduce topologically stable points, $β$-persistent points, $β$-persistent property, $β$-persistent measures and almost $β$-persistent measures for first countable Hausdorff group actions of compact metric spaces. We prove that the set of all $β$-persistent points is measurable and it is closed if the action is equicontinuous. We also prove that the set of all $β$-persistent measures is a convex set and every almost $β$-persistent measure is a $β$-persistent measure. Finally, we prove that every equicontinuous pointwise topologically stable first countable Hausdorff group action of a compact metric space is $β$-persistent. In particular, every equicontinuous pointwise topologically stable flow is $β$-persistent.
