Geodesic
Invariant measures on semigroups and imbedding topological semigroups in topological groups
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 277-284 
V. V. Mukhin. Invariant measures on semigroups and imbedding topological semigroups in topological groups. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 277-284. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a10/
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     title = {Invariant measures on semigroups and imbedding topological semigroups in topological groups},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the case of topological semigroups that are cancellative and right reversible is considered. It is shown (Theorem 1) that the existence in such a semigroup of a left invariant measure satisfying certain conditions is equivalent to the imbeddability of some open ideal of the given semigroup as an open subsemigroup in a locally compact group of left fractions. Conditions for imbedding topological semigroups in locally compact groups are considered in measure-theoretic terms. Bibliography: 8 titles.

[1] J. H. Williamson, “Harmonic analysis on semigroups”, J. London Math. Soc., 42:1 (1967), 1–41 | DOI | MR | Zbl

[2] A. Paterson, “Invariant measure semigroups”, Proc. London Math. Soc., 35:2 (1977), 313–332 | DOI | MR | Zbl

[3] R. Rigelhof, “Invariant measures on lokally compact semigroup”, Proc. Amer. Math. Soc., 28:1 (1971), 173–176 | DOI | MR | Zbl

[4] C. Gowrisankaran, “Semigroup with invariant Radon measures”, Proc. Amer. Math. Soc., 38:2 (1973), 400–404 | DOI | MR | Zbl

[5] A. B. Paalman–de Miranda, “Topological semigroups”, Math. Centre Tracts II, Math. Centrum, Amsterdam, 1970

[6] V. V. Mukhin, “O vlozhenii topologicheskikh polugrupp v topologicheskie gruppy”, VII vsesoyuznaya topologicheskaya konferentsiya, tezisy dokladov i soobschenii, 1977, 131

[7] P. Khalmosh, Teoriya mery, IL, Moskva, 1953

[8] N. Burbaki, Obschaya topologiya. Topologicheskie gruppy. Chisla i svyazannye s nimi, gruppy i prostranstva, izd-vo “Nauka”, Moskva, 1969 | MR