Journal of Symbolic Logic

Ultrafilters which Extend Measures

Michael Benedikt

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Abstract

We study classes of ultrafilters on $\omega$ defined by a natural property of the Loeb measure in the Nonstandard Universe corresponding to the ultrafilter. This class, the Property M ultrafilters, is shown to contain all ultrafilters built up by taking iterated products over collections of pairwise nonisomorphic selective ultrafilters. Results on Property M ultrafilters are applied to the construction of extensions of probability measures, and to the study of measurable reductions between ultrafilters.

Article information

Source
J. Symbolic Logic, Volume 63, Issue 2 (1998), 638-662.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745526

Mathematical Reviews number (MathSciNet)
MR1625895

Zentralblatt MATH identifier
0911.03033

JSTOR
links.jstor.org

Citation

Benedikt, Michael. Ultrafilters which Extend Measures. J. Symbolic Logic 63 (1998), no. 2, 638--662. https://projecteuclid.org/euclid.jsl/1183745526


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