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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DOI:
https://doi.org/10.1090/S0002-9939-1975-0382578-5

Article copyright:
© Copyright 1975
American Mathematical Society