Representation of measures via the standard part map

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Aldaz, Jesus Munarriz

Contributors dc:contributor

• Loeb, Peter A.

• Mathematics

Statement dc:rights

• Copyright 1991 Aldaz, Jesus Munarriz

Language dc:language

eng

Identifier

AAI9210722
(UMI)AAI9210722

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/22682