Summary
Let a regular Borel measure m on a locally compact semigroup S be upper semi-invariant i.e., m(C x)≧m(C) and m(x C)≧m(C) for every compact C and x in S. It is shown: (i) Every subsemigroup of S of positive measure contains an idempotent. (ii) S admits an upper semi-invariant probability measure iff S has a kernel K which is a compact group.
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Argabright, L. N.: A note on invariant integrals on locally compact semigroups. Proc. Amer. math. Soc. 17, 377–382(1966).
Kemperman, J. H. B.: On products of sets in a locally compact group. Fundamenta Math. 56, 57–61 (1964).
Rosen, W. G.: On invariant means over compact semigroups. Proc. Amer. math. Soc. 7, 1076–1082 (1956).
Tserpes, N. A., Kartsatos, A. G.: Mesures semi-invariantes sur un semigroupe localment compact. C. r. Acad. Sci. Paris 267, Sér. A 507–509 (1968).
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We should like to thank the referee for pointing out certain redundancies in the theorems. Also we thank Dr. Tze-Chien Sun for some helpful observations.
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Tserpes, N.A., Kartsatos, A.G. On semi-invariant probability measures on semigroups. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 260–262 (1970). https://doi.org/10.1007/BF00533296
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DOI: https://doi.org/10.1007/BF00533296