Elementary proofs of pointwise ergodic theorems for measure preserving transformations
The paper gives new (elementary) proofs of pointwise ergodic theorems for superadditive processes corresponding to measure preserving transformations. The construction in the paper is based on the application of the idea due to \textit{T.~Kamae} [Isr. J. Math. 42, 284-290 (1982; Zbl 0499.28011)] and \textit{P. C.~Shields} [IEEE Trans. Inf. Theory IT-33, 263-266 (1987; Zbl 0633.94004)]. The same idea was used recently in a new proof of Hopf's ratio ergodic theorem in the paper by \textit{T.~Kamae} and \textit{M.~Keane} [Osaka J. Math. 34, No. 3, 653-657 (1997; Zbl 0890.28010)]. The main tool actively used in the paper is the maximal ergodic theorem for superadditive processes.
scientific article; zbMATH DE number 1445754