On the ergodic theorem of E. Hopf (Q1310847)

The author extends the ergodic theorem of E. Hopf to a large class of Archimedean Riesz spaces. In order to obtain the extension, he defines and studies a new type of convergence in Archimedean Riesz spaces. The new type of convergence (which we call individual convergence) was inspired by a work of \textit{H. Nakano} [Ann. Math., II. Ser. 49, 538-556 (1948; Zbl 0032.35901)] (from which he also borrowed its name) and by a paper of \textit{D. Ornstein} [in ``Advances in probability and related topics'' 2, 85-115 (1970; Zbl 0321.28013)] on modifications and the ratio ergodic theorem.