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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariant measures on locally compact semigroups
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by Roger Rigelhof PDF
Proc. Amer. Math. Soc. 28 (1971), 173-176 Request permission

Abstract:

The main result of this paper shows that a locally compact abelian semigroup is embeddable as an open subsemigroup of a locally compact abelian group $G$ if and only if the translations $x \mapsto x + y$ are open maps and there exists a nonnegative regular measure $\mu$ on $S$ such that $\mu (U) = \mu (x + U) > 0$ for every open set $U$ and $x$ in $S$.
References
  • Nicolas Bourbaki, Éléments de mathématique. Fasc. II. Livre III: Topologie générale. Chapitre 1: Structures topologiques. Chapitre 2: Structures uniformes, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1142, Hermann, Paris, 1965 (French). Quatrième édition. MR 0244924
  • Robert Ellis, Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125. MR 88674
  • Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
  • Neal J. Rothman, Embedding of topological semigroups, Math. Ann. 139 (1960), 197–203 (1960). MR 116076, DOI 10.1007/BF01352911
  • J. H. Williamson, Harmonic analysis on semigroups, J. London Math. Soc. 42 (1967), 1–41. MR 208291, DOI 10.1112/jlms/s1-42.1.1
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 173-176
  • MSC: Primary 28.75; Secondary 42.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0277691-3
  • MathSciNet review: 0277691