Abstract and Applied Analysis

Nonstandard Methods in Measure Theory

Grigore Ciurea

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Ideas and techniques from standard and nonstandard theories of measure spaces and Banach spaces are brought together to give a new approach to the study of the extension of vector measures. Applications of our results lead to simple new proofs for theorems of classical measure theory. The novelty lies in the use of the principle of extension by continuity (for which we give a nonstandard proof) to obtain in an unified way some notable theorems which have been obtained by Fox, Brooks, Ohba, Diestel, and others. The methods of proof are quite different from those used by previous authors, and most of them are realized by means of nonstandard analysis.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 851080, 10 pages.

First available in Project Euclid: 2 October 2014

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Ciurea, Grigore. Nonstandard Methods in Measure Theory. Abstr. Appl. Anal. 2014 (2014), Article ID 851080, 10 pages. doi:10.1155/2014/851080. https://projecteuclid.org/euclid.aaa/1412277081

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