论文标题
具有SBM属性的几乎尼尔植物组的子集
Subsets of Virtually Nilpotent Groups with the SBM Property
论文作者
论文摘要
我们将满足标准间隔度量属性（SIM）属性的整数子集的概念扩展到了几乎nilpotent组的类别，并将相应属性命名为标准球度量（SBM）属性。为了做到这一点，我们在与此类组相关的渐近锥中定义了自然措施，并表明该度量满足了Lebesgue密度定理。然后，我们证明了已知在这种更广泛的上下文中已知的SIM卡的各种属性的类似物，偶尔假设该组的额外属性，例如小球属性和小间隙属性。
We extend Leth's notion of subsets of the integers satisfying the Standard interval measure (SIM) property to the class of virtually nilpotent groups and name the corresponding property the Standard ball measure (SBM) property. In order to do this, we define a natural measure on closed balls in asymptotic cones associated to such groups and show that this measure satisfies the Lebesgue density theorem. We then prove analogs of various properties known to hold for SIM sets in this broader context, occasionally assuming extra properties of the group, such as the small spheres property and the small gaps property.
