Representing measures in potential theory and an ideal boundary

zbMath1254.28015MaRDI QIDQ1928886

Peter A. Loeb

Publication date: 4 January 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1348505536

zbMATH Keywords

ideal boundaryLoeb measure spacesconstruction of representing measuresnonnegative harmonic functions

Mathematics Subject Classification ID

Martin boundary theory (31C35) Nonstandard models in mathematics (03H05) Nonstandard measure theory (28E05)

Cites Work

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• A construction of representing measures for elliptic and parabolic differential equations
• Applications of nonstandard analysis to ideal boundaries in potential theory
• A non-standard representation for Brownian motion and Ito integration
• The almost equivalence of pairwise and mutual independence and the duality with exchangeability
• A theory of hyperfinite processes: The complete removal of individual uncertainty via exact LLN
• Sturdy harmonic functions and their integral representations
• Nonstandard analysis in topology: nonstandard and standard compactifications
• An infinitesimal approach to stochastic analysis
• Adapted Probability Distributions
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• A Generalization of the Riesz-Herglotz Theorem on Representing Measures
• Weak Limits of Measures and the Standard Part Map
• A Nonstandard Characterization of Weak Convergence
• Hyperfinite Law of Large Numbers
• Purification and saturation
• Stochastic Processes Depending on a Continuous Parameter
• Non-standard analysis