Universal Loeb-Measurability of Sets and of the Standard Part Map with Applications

DOI10.2307/2000712zbMath0633.28009OpenAlexW4246275193MaRDI QIDQ3770751

Lothar Rogge, Dieter Landers

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000712

zbMATH Keywords

measure preserving transformationpre-near-standard pointsextension theorem for \(\tau \)-smooth Baire-measuresintegral measure algebraK-saturated modelsKakutani's product measure theoremLoeb measure algebra

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Nonstandard models in mathematics (03H05) Nonstandard measure theory (28E05)

Related Items (11)

Direct hyperfinite representations of finitely additive probabilities ⋮ Borel measure extensions of measures defined on sub-\(\sigma\)-algebras ⋮ Ergodicity of Markov Processes via Nonstandard Analysis ⋮ Compact Measures Have Loeb Preimages ⋮ \(\sigma\)-homomorphisms from the Borel \(\sigma\)-algebra into the Loeb \(\sigma\)-algebra ⋮ Inner and Outer Banach‐valued Loeb‐measures ⋮ The optimal control of nonlinear diffusion equations with rough initial data ⋮ Representing Abstract Measures by Loeb Measures: A Generalization of the Standard Part Map ⋮ Lifting Theorems in Nonstandard Measure Theory ⋮ Lower and upper Loeb-integrals ⋮ Gordon's conjectures 1 and 2: Pontryagin-van Kampen duality in the hyperfinite setting

Cites Work

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• Nonstandard Measure Theory and its Applications
• A functional approach to nonstandard measure theory
• Star-Finite Representations of Measure Spaces
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Analytic Sets, Baire Sets and the Standard Part Map
• Weak Limits of Measures and the Standard Part Map
• A Nonstandard Characterization of Weak Convergence
• Measures on Topological Spaces

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