Geodesic
On r*-Invariant Measure on a Locally Compact Semigroup with Recurrence
Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 237-239

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A regular Borel measure μ is said to be r*-invariant on a locally compact semigroup if μ(Ba -1) = μ(B) for all Borel sets B and points a of S, where Ba -1 ={xεS, xaεB}. In [1] Argabright conjectured that the support of an r*-invariant measure on a locally compact semigroup is a left group, Mukherjea and Tserpes [4] proved this conjecture in the case that the measure is finite; however their method of proof fails when the measure is infinite. 
Bourne, Samuel. On r*-Invariant Measure on a Locally Compact Semigroup with Recurrence. Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 237-239. doi: 10.4153/CMB-1980-032-x
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[1] 1. Argabright, L. N., A note on invariant integrals on locally compact semigroups, Proc. Amer. Math. Soc. 17 (1966), 377-382. Google Scholar

[2] 2. Berglund, J. F. and Hofmann, K. H., Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Mathematics 42, Springer-Verlag, Berlin, 1969. Google Scholar

[3] 3. Łos, L. and Schwarz, S., Remarks on compact semigroups, Colloq. Math. 6 (1958), 265-270. Google Scholar

[4] 4. Mukherjea, A. and Tserpes, N. A., Idempotent measures on locally compact semigroups, Proc. Amer. Math. Soc. 29 (1971), 143-150. Google Scholar

[5] 5. Sucheston, L., On existence of finite invariant measures, Math. Zeitschr. 86 (1964), 327-336. Google Scholar

[6] 6. Tserpes, N. A. and Mukherjea, A., On certain conjectures on invariant measures, Semigroup Forum 1 (1970), 260-266. Google Scholar

[7] 7. Wright, F. B.,The recurrence theorem, Amer. Math. Monthly 68 (1961), 247-278. Google Scholar

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