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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the measure theoretic structure
of compact groups


Authors: S. Grekas and S. Mercourakis
Journal: Trans. Amer. Math. Soc. 350 (1998), 2779-2796
MSC (1991): Primary 22C05, 28A35; Secondary 43A05
MathSciNet review: 1473441
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Abstract | References | Similar Articles | Additional Information

Abstract: If $G$ is a compact group with $w(G)=a\geq \omega$, we show the following results:

(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
(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

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02182-5
PII: S 0002-9947(98)02182-5
Keywords: Compact group, Haar measure, Baire isomorphism, Riemann integrable function, Jordan measurable set.
Received by editor(s): February 1, 1996
Article copyright: © Copyright 1998 American Mathematical Society