Open Access
2014 Nonstandard Methods in Measure Theory
Grigore Ciurea
Abstr. Appl. Anal. 2014: 1-10 (2014). DOI: 10.1155/2014/851080


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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Grigore Ciurea. "Nonstandard Methods in Measure Theory." Abstr. Appl. Anal. 2014 1 - 10, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023194
MathSciNet: MR3228091
Digital Object Identifier: 10.1155/2014/851080

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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