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Title:Representation of measures via the standard part map
Author(s):Aldaz, Jesus Munarriz
Doctoral Committee Chair(s):Loeb, Peter A.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:1991
Type:Text
Language:English
URI:http://hdl.handle.net/2142/22682
Rights Information:Copyright 1991 Aldaz, Jesus Munarriz
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9210722
OCLC Identifier:(UMI)AAI9210722


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