Weak limits of measures and the standard part map

Loeb, Peter A.

doi:10.1090/S0002-9939-1979-0539645-6

Weak limits of measures and the standard part map
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by Peter A. Loeb

Proc. Amer. Math. Soc. 77 (1979), 128-135

DOI: https://doi.org/10.1090/S0002-9939-1979-0539645-6

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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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