We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters. We explain how this implies certain equidistribution theorems which, even in a qualitative form, are not accessible to measure-classification theorems. As another application, we describe another proof of property tau for arithmetic groups.

中文翻译：

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有效均分和财产 ($\tau $)

我们证明了稳定器最大和半简单的 adelic 同质子集的定量等分布陈述。固定环境空间，语句所有参数统一。我们解释了这如何暗示某些等分布定理，即使是定性形式，度量分类定理也无法获得这些定理。作为另一个应用，我们描述了算术群的另一个性质 tau 的证明。