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Moving Ergodic Theorems for Superadditive Processes

Abstract Let be 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 averages where {FIn} is a superadditive process and {In} is a sequence of cubes in satisfying the "cone-condition". The identification of the limit is given. A moving local theorem is also proved.