论文标题
可衡量的嵌入式，免费产品和图形产品
Measurable Imbeddings, Free Products, and Graph Products
论文作者
论文摘要
我们研究了群体之间可衡量的嵌入性，这是对等效性的阶式概括，允许嵌入式群体具有无限的度量基本域。我们证明，如果$λ_1$可测量地嵌入$γ_1$中，而$λ_2$可在其他假设下，将相应的基本域以特殊方式安排在$γ_2$的情况下，然后$λ_1 *λ_1 *λ_2$可测量地iM imbays Immbays Imbeds中$γ__1 *γ___2$γ__2$。在我们使用的技术的基础上，我们表明类似结果适用于组的图形产品。
We study Measurable Imbeddability between groups, which is an order-like generalization of Measure Equivalence that allows the imbedded group to have an infinite measure fundamental domain. We prove if $Λ_1$ measurably imbeds into $Γ_1$, and $Λ_2$ measurably imbeds into $Γ_2$ under an additional assumption that lets the corresponding fundamental domains to be arranged in a special way, then $Λ_1 * Λ_2$ measurably imbeds into $Γ_1 * Γ_2$. Building upon the techniques we used, we show that the analogous result holds for graph products of groups.
