Von Neumann's mean ergodic theorem on complete random inner product modules (Q644538)

The authors continue investigations of T.\,Guo and his coauthors on random normed (and inner product) modules. The inner product module is a linear space \(S\) with a mapping \(\langle\cdot,\cdot \rangle\) from \(S\times S\) into a space \(L^0\) of all measurable functions on a probability space, with natural axioms. The authors prove two forms of von Neumann's mean ergodic theorem within the framework of complete random inner product modules, and present some applications.