# Ergodic Sequences in the Fourier-stieltjes Algebra and Measure Algebra of a Locally Compact Group

#### Abstract

Let G be a locally compact group. Blum and Eisenberg proved that if G is abelian, then a sequence of probability measures on G is strongly ergodic if and only if the sequence converges weakly to the Haar measure on the Bohr compactification of 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. 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.

### Cite this paper

@inproceedings{TOMING1998ErgodicSI, title={Ergodic Sequences in the Fourier-stieltjes Algebra and Measure Algebra of a Locally Compact Group}, author={ANTHONY TO-MING and V W Losert}, year={1998} }