Vol. 62, No. 1, 1976

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A characterization of topological left thick subsets in locally compact left amenable semigroups

James Chin-Sze Wong

Vol. 62 (1976), No. 1, 295–303

In this paper, we define the concept of topological left thick subsets in a locally compact semigroup which is a generalisation and extension of the concept of left thick subsets in (discrete) semigroups introduced by T. Mitchell and prove that if T is a Borel measurable subset of a locally compact left amenable semigroup S, then T is topological left thick if and only if there is a topological left invariant mean M on S such that M(χT) = 1 where χT is the characteristic functional of T in S, thus generalising, and extending a result of Mitchell for (discrete) semigroup.

Mathematical Subject Classification 2000
Primary: 43A07
Received: 8 July 1975
Published: 1 January 1976
James Chin-Sze Wong