Representation of measures via the standard part map
Aldaz, Jesus Munarriz
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https://hdl.handle.net/2142/22682
Description
Title
Representation of measures via the standard part map
Author(s)
Aldaz, Jesus Munarriz
Issue Date
1991
Doctoral Committee Chair(s)
Loeb, Peter A.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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