A simple proof of Wiener's multiparameter ergodic theorem is given in this paper. At the same time it is shown that two of the hypotheses of an existing proof can be dispensed with.
"Multiparameter Groups of Measure-Preserving Transformations: A Simple Proof of Wiener's Ergodic Theorem." Ann. Probab. 9 (3) 504 - 509, June, 1981. https://doi.org/10.1214/aop/1176994423