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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unbounded Loeb measures


Author: C. Ward Henson
Journal: Proc. Amer. Math. Soc. 74 (1979), 143-150
MSC: Primary 28B99; Secondary 03H05
DOI: https://doi.org/10.1090/S0002-9939-1979-0521888-9
MathSciNet review: 521888
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Abstract: Uniqueness of the Carathéodory extension is proved for the unbounded case of Loeb's measure space construction in nonstandard analysis and these measures are studied. Methods are developed for handling sets in the $ \sigma $-algebra generated by the internal sets. A quantitative theory of degrees of null measure is developed.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0521888-9
Article copyright: © Copyright 1979 American Mathematical Society