Uniform logical new proofs for the Daniell-Stone theorem and the Riesz representation theorem

DOI10.1007/s41980-021-00662-zOpenAlexW4206734057WikidataQ113890899 ScholiaQ113890899MaRDI QIDQ2081667

Alireza Mofidi

Publication date: 30 September 2022

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.03774

zbMATH Keywords

Riesz representation theorempositive functionalsDaniell-Stone theorem for Daniell integralsintegration logiclogical compactness theorem

Mathematics Subject Classification ID

Integration with respect to measures and other set functions (28A25) Logic with extra quantifiers and operators (03C80) Applications of model theory (03C98) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05)

Cites Work

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• On some dynamical aspects of NIP theories
• Nonstandard integration theory in topological vector lattices
• The logic of integration
• Haar measure and integral logic
• Another ‘short’ proof of the Riesz representation theorem
• Random variables and integral logic
• Quantified universes and ultraproducts
• The Baire and Borel measure
• The Riesz Representation Theorem Revisited
• A Simple Proof of the Daniel-Stone Representation Theorem
• Yet another short proof of the Riesz representation theorem
• Probability logic
• The Nonstandard Theory of Topological Vector Spaces

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