Egoroff's theorem and the distribution of standard points in a nonstandard model

Authors:
C. Ward Henson and Frank Wattenberg

Journal:
Proc. Amer. Math. Soc. **81** (1981), 455-461

MSC:
Primary 03H05; Secondary 26E35, 28A12

DOI:
https://doi.org/10.1090/S0002-9939-1981-0597662-3

MathSciNet review:
597662

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Abstract: We study the relationship between the Loeb measure of a set and the -measure of the set of standard points in . If is in the -algebra generated by the standard sets, then . This is used to give a short nonstandard proof of Egoroff's Theorem. If is an internal, * measurable set, then in general there is no relationship between the measures of and . However, if is an ultrapower constructed using a minimal ultrafilter on , then implies that is a -null set. If, in addition, is a Borel measure on a compact metric space and is a Loeb measurable set, then

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0597662-3

Article copyright:
© Copyright 1981
American Mathematical Society