We undertake a comprehensive study of measure equivalence between general locally compact, second countable groups, providing operator algebraic and ergodic theoretic reformulations, and complete the classification of amenable groups within this class up to measure equivalence.

中文翻译：

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非等距群的度量等价

我们对一般局部紧致，第二可数组之间的等价度量进行了全面研究，提供了算子代数和遍历的理论公式，并完成了该类中可度量类的分类，以衡量等值。