On the measure theoretic structure of compact groups
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- by S. Grekas and S. Mercourakis PDF
- Trans. Amer. Math. Soc. 350 (1998), 2779-2796 Request permission
Abstract:
If $G$ is a compact group with $w(G)=a\geq \omega$, we show the following results:
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[(i)] There exist direct products $\displaystyle {\prod _{\xi <a}G_{\xi }, \prod _{\xi <a}H_{\xi }}$ of compact metric groups and continuous open surjections $\displaystyle {\prod _{\xi <a}G_{\xi } \stackrel {p}{\rightarrow }G \stackrel {q}{\rightarrow }\prod _{\xi <a}H_{\xi }}$ with respect to Haar measure; and
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[(ii)] the Haar measure on $G$ is Baire and at the same time Jordan isomorphic to the Haar measure on a direct product of compact Lie groups.
Applications of the above results in measure theory are given.
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Additional Information
- S. Grekas
- Affiliation: Department of Mathematics, University of Athens, Panepistemiopolis, 157 84 Athens, Greece
- Email: sgrekas@eudoxos.dm.uoa.gr
- S. Mercourakis
- Affiliation: Department of Mathematics, University of Athens, Panepistemiopolis, 157 84 Athens, Greece
- Email: smerkour@eudoxos.dm.uoa.gr
- Received by editor(s): February 1, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 2779-2796
- MSC (1991): Primary 22C05, 28A35; Secondary 43A05
- DOI: https://doi.org/10.1090/S0002-9947-98-02182-5
- MathSciNet review: 1473441