Nonstandard theory of vector measures

Ideas and techniques from nonstandard theories of measure spaces and Banach spaces are brought together to develop a nonstandard theory of Banach space valued measures. In particular, constructions of countably additive vector measures from internal vector measures are presented. An integration theory of real valued functions with respect to Banach space valued measures is also developed. Applications include direct constructions of representing measures of both absolutely summing operators and weakly compact operators, as well as solutions of problems concerning the range of a vector measure.

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

• Sun, Ye Neng

Contributors dc:contributor

• Uhl, J. Jerry, Jr.

• Mathematics

Statement dc:rights

• Copyright 1989 Sun, Ye Neng

Language dc:language

eng

Identifier

AAI9011043
(UMI)AAI9011043

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/22001