Journal of Symbolic Logic

Ultrafilters which Extend Measures

Michael Benedikt

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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.

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

First available in Project Euclid: 6 July 2007

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Benedikt, Michael. Ultrafilters which Extend Measures. J. Symbolic Logic 63 (1998), no. 2, 638--662.

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