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Uhl, J. Jerry, Jr. Sun, Ye Neng 2011-05-07T13:25:47Z 2011-05-07T13:25:47Z 10000-01-01 1989 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. Made available in DSpace on 2011-05-07T13:25:47Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9011043.pdf: 2639110 bytes, checksum: 91f1b2b2feb1f73af0139d185499da0b (MD5) Previous issue date: 1989 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:39Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:25:25-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9011043 (UMI)AAI9011043 http://hdl.handle.net/2142/22001 eng Copyright 1989 Sun, Ye Neng Mathematics Nonstandard theory of vector measures text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.