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Abstract and Applied Analysis
Volume 2014, Article ID 851080, 10 pages
Research Article

Nonstandard Methods in Measure Theory

Mathematics Department, Academy of Economic Studies, Piata Romana 6, 010374 Bucharest, Romania

Received 14 January 2014; Accepted 28 April 2014; Published 26 June 2014

Academic Editor: Geraldo Botelho

Copyright © 2014 Grigore Ciurea. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.