Star-Finite Representations of Measure Spaces
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Publication:3957177
DOI10.2307/1998904zbMath0494.28005OpenAlexW4243722329MaRDI QIDQ3957177
Publication date: 1982
Full work available at URL: https://doi.org/10.2307/1998904
compactificationintegralsuniform integrabilitynonstandard analysisconditional expectationsmeasure spacesRadon spaces*-finite modelsmeasure-preserving images of *- finite measure spaces
Set functions and measures on topological spaces (regularity of measures, etc.) (28C15) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05) Nonstandard analysis (26E35)
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Cites Work
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- Applications of nonstandard analysis to ideal boundaries in potential theory
- A non-standard representation for Brownian motion and Ito integration
- Lectures on non-standard analysis
- Conditional probability can be defined for all pairs of sets of reals
- Victoria symposium on nonstandard analysis. University of Victoria 1972
- Mean Convergence of Martingales
- Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations.I
- Hyperdefinite stochastic integration III: Hyperdefinite representations of standard martingales.
- Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
- Nonstandard Measure Theory: Avoiding Pathological Sets
- Probability logic
- Weak Limits of Measures and the Standard Part Map
- A Nonstandard Characterization of Weak Convergence
- A nonstandard representation of measurable spaces and 𝐿_{∞}
- On the Nonstandard Representation of Measures