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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An example in the Weil theory of measurable groups


Author: Robert E. Atalla
Journal: Proc. Amer. Math. Soc. 25 (1970), 816-819
MSC: Primary 28.75; Secondary 22.00
MathSciNet review: 0271308
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Abstract: According to a theorem of Andre Weil, if a group $ G$ possesses an invariant measure which satisfies certain conditions, in particular measurability of the map $ (x,y) \to (x,xy)$ of $ G \times G$, then $ G$ has a locally bounded Hausdorff topology making $ G$ a topological group. We offer a simple counterexample to show the need for the above stated condition.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0271308-9
PII: S 0002-9939(1970)0271308-9
Keywords: Topological group, measurable group, Haar measure, invariant measure, Weil topology
Article copyright: © Copyright 1970 American Mathematical Society