标题： 精确性与不变随机等价关系空间的拓扑学 显示英文标题

标题： Exactness and the topology of the space of invariant random equivalence relations

摘要： 我们通过在$\Gamma$上的不变随机等价关系（IREs）来表征可数群$\Gamma$的精确性。 具体来说，我们证明了$\Gamma$是精确的当且仅当每个有限 IRE 的弱极限是一个可约的 IRE。 特别地，对于精确群而言，这说明与理想伯努利沃罗诺伊镶嵌相关的受限重根关系是可约的，这是理想泊松沃罗诺伊镶嵌的离散版本。 显示英文摘要

摘要： We characterize exactness of a countable group $\Gamma$ in terms of invariant random equivalence relations (IREs) on $\Gamma$. Specifically, we show that $\Gamma$ is exact if and only if every weak limit of finite IREs is an amenable IRE. In particular, for exact groups this implies amenability of the restricted rerooting relation associated to the ideal Bernoulli Voronoi tessellation, the discrete analog of the ideal Poisson Voronoi tesselation.