Completely additive measure and integration

Shorb, Alan McK.

doi:10.1090/S0002-9939-1975-0382578-5

Completely additive measure and integration

Author: Alan McK. Shorb
Journal: Proc. Amer. Math. Soc. 53 (1975), 453-459
MSC: Primary 28A10; Secondary 02H25
DOI: https://doi.org/10.1090/S0002-9939-1975-0382578-5
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 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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