Ergodic sequences in the Fourier-Stieltjes algebra and measure algebra of a locally compact group

Abstract

Let G G be a locally compact group. Blum and Eisenberg proved that if G G is abelian, then a sequence of probability measures on G G is strongly ergodic if and only if the sequence converges weakly to the Haar measure on the Bohr compactification of G . G. In this paper, we shall prove an extension of Blum and Eisenberg’s Theorem for ergodic sequences in the Fourier-Stieltjes algebra of G . G. We shall also give an improvement to Milnes and Paterson’s more recent generalization of Blum and Eisenberg’s result to general locally compact groups, and we answer a question of theirs on the existence of strongly (or weakly) ergodic sequences of measures on G . G.