The structure of limit measures and their supports on topological semigroups

Given a sequence of measures (μ _n ) on a topological semigroupS, a measure λ onS is called a tail limit of (μ _n ) if for some subsequence of integers (n _i ), converges weakly to ν _k for allk and λ is a weak limit point of the sequence (ν _k ). The main theorem of this paper characterizes the supports of the tail limits on compact completely simple semigroups. Some applications of the theorem and various open problems are discussed.