论文标题
无数量度理论的基本方面：Gelfand二元性，Riesz表示，规范模型和规范瓦解
Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration
论文作者
论文摘要
我们收集了几个基本结果，涉及本地紧凑的空间，概率空间和概率代数，以及可交付的$ C^*$ - 代数和von Neumann代数，配备了“无形的”设置，其中没有可分离性，Metriesible，Metriesible，Metriesibles，或者将标准的Borel假设放在这些空间上。特别是，我们回顾了本种环境中可用的gelfand二元性和riesz表示定理。我们还提出了一个规范模型，该模型代表概率代数为紧凑的Hausdorff概率空间，并以完全功能的方式使用该模型，并应用此模型来获得规范分解定理并轻松构建各种产品测量。这些工具可用于应用“无数”的恒星理论（如作者和其他理论所证明的那样）。
We collect several foundational results regarding the interaction between locally compact spaces, probability spaces and probability algebras, and commutative $C^*$-algebras and von Neumann algebras equipped with traces, in the "uncountable" setting in which no separability, metrizability, or standard Borel hypotheses are placed on these spaces and algebras. In particular, we review the Gelfand dualities and Riesz representation theorems available in this setting. We also present a canonical model that represents probability algebras as compact Hausdorff probability spaces in a completely functorial fashion, and apply this model to obtain a canonical disintegration theorem and to readily construct various product measures. These tools are useful in applications to "uncountable" ergodic theory (as demonstrated by the authors and others).
