标题： 测度等价和索菲克逼近 显示英文标题

标题： Measure equivalence and sofic approximations

摘要： 我们介绍一种技术，用于从它们的sofic近似之间的映射族中生成两个sofic群之间的测度耦合。 我们利用这一点来构建满足预定可积性条件的群对之间的测度耦合。 作为应用，我们证明了可解的Baumslag-Solitar群、灯工群和SOL群彼此之间都是指数测度等价的：特别是它们对于所有p都是L^p测度等价的。这与这些群通常不是彼此拟等距的事实形成鲜明对比：事实上，例如，灯组为Z/3Z的灯工群并不拟等距于灯组为Z/2Z的灯工群。 显示英文摘要

摘要： We introduce a technique for producing a measure coupling between two sofic groups from a family of maps between their sofic approximations. We exploit this to construct measure couplings between pairs of groups with prescribed integrability conditions. As an application we show that solvable Baumslag-Solitar groups, Lamplighters and the group SOL are all exponentially measure equivalent to one another: in particular they are L^p measure equivalent for all p. This is in sharp contrast with the fact that these groups are in general not quasi-isometric to one another: indeed, for instance the lamplighter with lamp group Z/3Z is not quasi-isometric the lamplighter with lamp group Z/2Z.