Almost everywhere convergence of ergodic averages of nonlinear operators (Q1891789)

The author considers order preserving mappings \(T\), which are nonexpansive in \(L^1\) and \(L^\infty\), and obtains two principal, mutually equivalent results. The almost everywhere convergence of \({T^nf\over n}\) (primarily of interest if \(T0\neq 0\)) and the ergodic averages \({S_nf\over n+1}\), where \(S_0f=f\), \(S_{n+1}f= f+TS_nf\).