Moving Ergodic Theorems for Superadditive Processes

Abstract

AbstractLetbe a semigroup of measure preserving transformations on a measure space (Ω, ℱ, μ). The main result of the paper is the proof of a.e. convergence for the moving averageswhere {FIn} is a superadditive process and {In} is a sequence of cubes insatisfying the "cone-condition". The identification of the limit is given. A moving local theorem is also proved.