Weak Limits of Measures and the Standard Part Map

DOI10.2307/2042730zbMath0394.03061OpenAlexW2058739022MaRDI QIDQ4175284

Peter A. Loeb

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/2042730

zbMATH Keywords

nonstandard analysisBorel setnonstandard measure theorycompact Hausdorff spacestandard part maptight measureweak cluster pointinternal Baire measurekolmogorov extension theoremriesz-herglotz theoremweak limits of measures

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Real- or complex-valued set functions (28A10) Compactness (54D30) Convergence of probability measures (60B10) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Nonstandard models in mathematics (03H05) Nonstandard analysis (26E35) Nonstandard topology (54J05)

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Cites Work

• Applications of nonstandard analysis to spin models
• Applications of nonstandard analysis to ideal boundaries in potential theory
• A non-standard representation for Brownian motion and Ito integration
• 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
• A Generalization of the Riesz-Herglotz Theorem on Representing Measures
• A Nonstandard Characterization of Weak Convergence
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