An example in the Weil theory of measurable groups
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- by Robert E. Atalla
- Proc. Amer. Math. Soc. 25 (1970), 816-819
- DOI: https://doi.org/10.1090/S0002-9939-1970-0271308-9
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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.References
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 816-819
- MSC: Primary 28.75; Secondary 22.00
- DOI: https://doi.org/10.1090/S0002-9939-1970-0271308-9
- MathSciNet review: 0271308