Nonstandard integration theory in topological vector lattices

DOI10.1007/BF01320737zbMath0890.46059MaRDI QIDQ1361001

Peter A. Loeb, Horst Osswald

Publication date: 23 July 1997

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178782

zbMATH Keywords

Bochner integralmonotone convergence theoremtopological vector latticesDaniell-Stone integration theorynonstandard hull valued integral

Mathematics Subject Classification ID

Vector-valued measures and integration (46G10) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Nonstandard models in mathematics (03H05) Nonstandard functional analysis (46S20) Ordered topological linear spaces, vector lattices (46A40) Nonstandard measure theory (28E05) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05)

Related Items (3)

Malliavin calculus in abstract Wiener space using infinitesimals ⋮ Uniform logical new proofs for the Daniell-Stone theorem and the Riesz representation theorem ⋮ The Gould integral in Banach lattices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A regular metrizable boundary for solutions of elliptic and parabolic differential equations
• On the theory of vector valued Loeb measures and integration
• Applications of nonstandard analysis to ideal boundaries in potential theory
• A non-standard representation for Brownian motion and Ito integration
• Harmonic spaces and their potential theory
• On generalized limits and linear functionals
• On the Extensions of Vector-Valued Loeb Measures
• A Combinatorial Analog of Lyapunov's Theorem for Infinitesimally Generated Atomic Vector Measures
• A functional approach to nonstandard measure theory
• Vector valued Loeb measures and the Lewis integral.
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• A Nonstandard Characterization of Weak Convergence
• An extension of the Bochner integral generalizing the Loeb–Osswald integral
• The Nonstandard Theory of Topological Vector Spaces
• Integration of Correspondences on Loeb Spaces
• Stochastic Navier-Stokes equations

This page was built for publication: Nonstandard integration theory in topological vector lattices