Joint ergodicity of actions of an abelian group (Q2925268)

Joint ergodicity for a collection of measure-preserving transformations was studied by \textit{D. Berend} [J. Anal. Math. 45, 255--284 (1985; Zbl 0595.28020)] and \textit{D. Berend} and \textit{V. Bergelson} [Isr. J. Math. 56, 123--128 (1986; Zbl 0619.28012)] as a generalization of the notions of ergodicity itself. Here, some new results are given for the notions of joint and total ergodicity for actions of countable abelian groups. For a finite collection of actions of a countable abelian group, it is shown that joint ergodicity of the collection implies total joint ergodicity if each of the actions is totally ergodic. Examples are given to show that joint ergodicity does not imply total joint ergodicity in general.