Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Invariant measures on locally compact semigroups


Author: Roger Rigelhof
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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 https://doi.org/10.1007/BF01352911
  • J. H. Williamson, Harmonic analysis on semigroups, J. London Math. Soc. 42 (1967), 1–41. MR 208291, DOI https://doi.org/10.1112/jlms/s1-42.1.1

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28.75, 42.00

Retrieve articles in all journals with MSC: 28.75, 42.00


Additional Information

Keywords: Invariant measures, Haar measures, locally compact abelian semigroups, topological semigroups
Article copyright: © Copyright 1971 American Mathematical Society