Elementary proofs of pointwise ergodic theorems for measure preserving transformations
type: Item
instance of: scholarly article
title: Elementary proofs of pointwise ergodic theorems for measure preserving transformations
zbMATH Open document ID: 0957.28007
published in: Osaka Journal of Mathematics
publication date: 2001-03-07T00:00:00Z
review text: 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.
reviewed by: Michael L. Blank
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 1445754
zbMATH Keywords: ergodic theorem
zbMATH Keywords: superadditive process
zbMATH Keywords: invariant measure
author: Ryotaro Sato
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1445754