论文标题
类固醇的不适和卷积能力的渐近不变性
Amenability of groupoids and asymptotic invariance of convolution powers
论文作者
论文摘要
冯·诺伊曼（von Neumann）在高度非构造术语中给出的舒适性的原始定义以后使用近似不变的概率度量进行重铸。此外，正如Furstenberg猜想的那样，Kaimanovich-Vershik和Rosenblatt证明了它，局部紧凑型组的不适应实际上与该组对具有其卷积能力序列的属性的单个概率度量的存在相当于不变的。在本文中，我们扩展了对测量类固醇的特征。它特别意味着，保存小组动作的度量类别的不适应等于存在于动作空间参数参数的群体上的随机环境，因此几乎每个环境中随机行走的尾巴都是微不足道的。
The original definition of amenability given by von Neumann in the highly non-constructive terms of means was later recast by Day using approximately invariant probability measures. Moreover, as it was conjectured by Furstenberg and proved by Kaimanovich-Vershik and Rosenblatt, the amenability of a locally compact group is actually equivalent to the existence of a single probability measure on the group with the property that the sequence of its convolution powers is asymptotically invariant. In the present article we extend this characterization of amenability to measured groupoids. It implies, in particular, that the amenability of a measure class preserving group action is equivalent to the existence of a random environment on the group parameterized by the action space, and such that the tail of the random walk in almost every environment is trivial.
