论文标题
可衡量的无环的局部可计数鲍尔图的完美匹配
Measurable perfect matchings for acyclic locally countable Borel graphs
论文作者
论文摘要
我们表征了无环的局部可数鲍勒图的结构障碍，这些borel完美匹配是从其连接的组件中选择有限的许多目的的Borel选择。特别是，这产生了至少三个学位图的Borel匹配。作为推论，可以得出至少三个生成$μ$ $ hyperfinite等价关系的无环局部可计数的borel图。我们在本地有限的情况下建立了Baire可测量匹配的类似结果，并在本地可计数的情况下提供了反例。
We characterize the structural impediments to the existence of Borel perfect matchings for acyclic locally countable Borel graphs admitting a Borel selection of finitely many ends from their connected components. In particular, this yields the existence of Borel matchings for such graphs of degree at least three. As a corollary, it follows that acyclic locally countable Borel graphs of degree at least three generating $μ$-hyperfinite equivalence relations admit $μ$-measurable matchings. We establish the analogous result for Baire measurable matchings in the locally finite case, and provide a counterexample in the locally countable case.
