Analytic Mappings on Hyperfinite Sets

DOI10.2307/2160342zbMath0784.03038OpenAlexW4248363969MaRDI QIDQ5288070

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Publication date: 5 April 1994

Full work available at URL: https://doi.org/10.2307/2160342

zbMATH Keywords

analytic setshyperfinite setsanalytic partial functionsextensions of internal set functions to capacitiesnonexistence of ergodic Borel transformations of a Loeb probability space

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Descriptive set theory (03E15) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Nonstandard models in mathematics (03H05) Nonstandard measure theory (28E05) Nonstandard analysis (26E35)

Related Items (6)

Hyperfinite transversal theory. II ⋮ Every Borel function is monotone Borel ⋮ Borel measure extensions of measures defined on sub-\(\sigma\)-algebras ⋮ Graphs with \(\boldsymbol\Pi^ 0_ 1(\kappa)\) \(Y\)-sections ⋮ Lifting Theorems in Nonstandard Measure Theory ⋮ Distinguishing three strong saturation properties in nonstandard analysis

Cites Work

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• Every Borel function is monotone Borel
• Some results about Borel sets in descriptive set theory of hyperfinite sets
• Descriptive set theory over hyperfinite sets
• Lifting Theorems in Nonstandard Measure Theory
• The structure of graphs all of whose Y-sections are internal sets
• U-meager sets when the cofinality and the coinitiality of U are uncountable
• Uniqueness of Unbounded Loeb Measure Using Choquet's Theorem
• The isomorphism property in nonstandard analysis and its use in the theory of Banach spaces
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Analytic Sets, Baire Sets and the Standard Part Map
• Unbounded Loeb Measures

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