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• W3089621865 abstract "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)." @default.
• W3089621865 created "2020-10-08" @default.
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• W3089621865 date "2020-10-01" @default.
• W3089621865 modified "2023-09-25" @default.
• W3089621865 title "Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration" @default.
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• W3089621865 doi "https://doi.org/10.48550/arxiv.2010.00681" @default.
• W3089621865 hasPublicationYear "2020" @default.
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