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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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
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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