论文标题
度量和强大性的渐近扩张
Asymptotic expansion in measure and strong ergodicity
论文作者
论文摘要
在本文中，我们介绍并研究了可衡量作用的渐近扩展的概念。这将概括地扩展，并就强大的经典概念提供了新的观点。此外，我们获得了渐近扩展动作的结构定理，表明它们允许扩展领域的疲惫。作为应用程序，我们恢复了马拉基（Marrakchi）的最新结果，其特征在局部光谱差距方面表征了强烈的遗传性。我们还表明，同质性强烈的行动始终在度量方面扩大，并通过近似空间在度量中建立渐近扩张和渐近扩张器之间的联系。
In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalises expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterising strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.
