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Representation of measures via the standard part map

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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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