无限测度保持设定下布尔作用的空间模型
Spatial models for boolean actions in the infinite measure-preserving setup
AI总结：
本文证明局部紧波兰群的无限测度保持作用可转化为Radon测度下的连续空间作用，推广了点实现定理，并精简证明了局部有限测度下Lévy群无非平凡连续测度保持作用。
摘要：
我们证明，在相差一个零集的意义下，局部紧波兰群的每个无限测度保持作用均可转化为在局部紧波兰空间上的连续测度保持作用，且其底层测度为Radon测度。我们还研究了无限测度保持设定下空间作用与布尔作用之间的区别。特别地，我们将Kwiatkowska和Solecki的点实现定理推广至无限测度设定。最后，我们给出了Avraham-Re'em和Roy近期结果的一个精简证明：当测度局部有限时，Lévy群无法在波兰空间上 admits 非平凡的连续测度保持作用。
英文摘要：
We show that up to a null set, every infinite measure-preserving action of a locally compact Polish group can be turned into a continuous measure-preserving action on a locally compact Polish space where the underlying measure is Radon. We also investigate the distinction between spatial and boolean actions in the infinite measure-preserving setup. In particular, we extend Kwiatkowska and Solecki's Point Realization Theorem to the infinite measure setup. We finally obtain a streamlined proof of a recent result of Avraham-Re'em and Roy: Lévy groups cannot admit nontrivial continuous measure-preserving actions on Polish spaces when the measure is locally finite.
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