Ergodic sequences of probability measures on commutative hypergroups (Q1774664)

An analogue of a result of \textit{J. Blum} and \textit{B. Eisenberg} [Proc. Am. Math. Soc. 42, 423--429 (1974; Zbl 0252.43002)] concerning strongly ergodic sequences (generalized summing sequences) on locally compact abelian groups is proved in this paper in the setting of commutative hypergroups. In the Blum-Eisenberg's result an equivalent condition for the strong ergodicity of a sequence is the weak convergence to the Haar measure on the Bohr compactification of the group. Since the Bohr compactification of a hypergroup does not necessarily carry an extending hypergroup structure, that condition is replaced in this paper by the weak*-convergence to the unique invariant mean on the closure of the linear span of the set of coefficient functions of the representations of the commutative hypergroup.