| Title: | Nonstandard theory of vector measures |
| Author(s): | Sun, Ye Neng |
| Doctoral Committee Chair(s): | Uhl, J. Jerry, Jr. |
| Department / Program: | Mathematics |
| Discipline: | Mathematics |
| Degree Granting Institution: | University of Illinois at Urbana-Champaign |
| Degree: | Ph.D. |
| Genre: | Dissertation |
| Subject(s): | Mathematics |
| Abstract: | 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. |
| Issue Date: | 1989 |
| Type: | Text |
| Language: | English |
| URI: | http://hdl.handle.net/2142/22001 |
| Rights Information: | Copyright 1989 Sun, Ye Neng |
| Date Available in IDEALS: | 2011-05-07 |
| Identifier in Online Catalog: | AAI9011043 |
| OCLC Identifier: | (UMI)AAI9011043 |
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