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

 

Weak limits of measures and the standard part map


Author: Peter A. Loeb
Journal: Proc. Amer. Math. Soc. 77 (1979), 128-135
MSC: Primary 28A99; Secondary 03H05, 60B10
MathSciNet review: 539645
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Abstract: A construction is given, using the standard part map st, of the $ {\text{weak}^\ast}$ standard part of an internal Baire measure in the nonstandard extension of a compact Hausdorff space. It is shown that the inverse image with respect to st of a Borel set is universally measurable with respect to completions of the $ \sigma $-algebra generated by internal Baire sets. Applications and extensions of these results to noncompact spaces are given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0539645-6
PII: S 0002-9939(1979)0539645-6
Keywords: Nonstandard analysis, $ {\text{weak}^\ast}$ standard part, $ {\text{weak}^\ast}$ cluster point, Kolmogorov extension theorem, Riesz-Herglotz theorem, tight measure
Article copyright: © Copyright 1979 American Mathematical Society