Representation of measures via the standard part map
type: CreativeWork
description: In this dissertation we study the representation of standard measures and contents via Loeb measures and the standard part map, extending previously known results to a nontopological setting. In addition, a characterization of the completely regular and Hausdorff spaces which are universally Loeb measurable is given. Applications of these techniques include a new nonstandard proof of the Riesz Representation Theorem, as well as the construction of the projective hull, an object akin to the projective limit of a projective system of measure spaces. Loeb's functional approach to nonstandard measure theory is also considered, and a simplification of his work is proposed.
abstract: In this dissertation we study the representation of standard measures and contents via Loeb measures and the standard part map, extending previously known results to a nontopological setting. In addition, a characterization of the completely regular and Hausdorff spaces which are universally Loeb measurable is given. Applications of these techniques include a new nonstandard proof of the Riesz Representation Theorem, as well as the construction of the projective hull, an object akin to the projective limit of a projective system of measure spaces. Loeb's functional approach to nonstandard measure theory is also considered, and a simplification of his work is proposed.
author: Aldaz, Jesus Munarriz
language: eng
keywords: Mathematics
date published: 2011-05-07T13:47:56Z
date modified: 2026-07-22T22:25:20Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/22682