论文标题
有限规模和财产
Bounded Scale Measure and Property A
论文作者
论文摘要
我们引入了一个有界几何形状的概括，我们称之为有限的比例度量。我们表明，与有限的几何形状不同，有界尺度度量是一种粗糙的不变。然后，我们显示了具有有界比例度量的空间的等效定义，并显示了具有界限尺寸度量满足的其他属性。从那里，我们将属性a从统一离散的度量空间概括为具有有界几何形状的大规模空间。最后，我们为具有有界比例尺度量的大型空间构建属性A的定义，并表明属性A的定义是粗糙的不变。
We introduce a generalization for bounded geometry that we call bounded scale measure. We show that bounded scale measure is a coarse invariant unlike bounded geometry. We then show equivalent definitions for spaces with bounded scale measure and show other properties that spaces with bounded scale measure satisfy. From there, we generalize property A from uniformly discrete metric spaces to large scale spaces with bounded geometry. Lastly, we construct a definition for property A for large scale spaces with bounded scale measure and show that this definition of property A is a coarse invariant.
