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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Completely additive measure and integration


Author: Alan McK. Shorb
Journal: Proc. Amer. Math. Soc. 53 (1975), 453-459
MSC: Primary 28A10; Secondary 02H25
MathSciNet review: 0382578
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Abstract: This paper is an extension of the efforts to cast the theory of measure and integration into the framework of nonstandard analysis, begun by Robinson [7, particularly Theorem 3.5.2], and continued by Bernstein and Wattenberg, Loeb and Henson. The principal result, Theorem 3, is: There exists a completely additive measure function defined on all subsets of $ R$ which nearly agrees with Lebesgue measure and is nearly translation invariant on bounded sets. Its integral is defined for all sets and functions, and nearly agrees with the Lebesgue integral.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0382578-5
PII: S 0002-9939(1975)0382578-5
Article copyright: © Copyright 1975 American Mathematical Society