Nonstandard theory of vector measures

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Title:	Nonstandard theory of vector measures
Author(s):	Sun, Ye Neng
Doctoral Committee Chair(s):	Uhl, Jerry J.
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