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Analytic Sets, Baire Sets and the Standard Part Map

Published online by Cambridge University Press:  20 November 2018

C. Ward Henson
C. Ward Henson*
Affiliation:
University of Illinois at Urbana–Champaign, Urbana, Illinois
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The problems considered here arose in connection with the interesting use by Loeb [8] and Anderson [1], [2] of Loeb's measure construction [7] to define measures on certain topological spaces. The original problem, from which the results given here developed, was to identify precisely the family of sets on which these measures are defined.

To be precise, let be a set theoretical structure and * a nonstandard extension of , as in the usual framework for nonstandard analysis (see [10]). Let X be a Hausdorff space in and stx the standard part map for X, defined on the set of nearstandard points in *X. Suppose, for example, µ is an internal, finitely additive probability measure defined on the internal subsets of *X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 663 - 672
Copyright
Copyright © Canadian Mathematical Society 1979

References

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