The Size of the Set of Left Invariant Means on an Ela Semigroup

Alan L. T. Paterson
1978 Proceedings of the American Mathematical Society  
Let 5 be an ELA semigroup and let m(S) be the smallest possible cardinality of the set {s 6 S: Fs = {s)) as F ranges over the finite subsets of S. The main purpose of this note is to show that if m(S) is infinite, then S has exactly 22" (multiplicative) left invariant means.
doi:10.2307/2042534 fatcat:j2pqurciefel5db52gd433bbom