Journal Article10.4153/CJM-1995-038-3
Moving ergodic theorems for superadditive processes
TL;DR: In this article, the convergence of the moving average #/ǫ is proved for a semigroup of measure-preserving transformations on a measure space (Q, f, ji).
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Abstract: Let T = (ju)uçjd be a semigroup of measure preserving transformations on a measure space (Q, f, ji). The main result of the paper is the proof of a.e. convergence for the moving averages #/„ where {Fjn} is a superadditive process and {/„} is a sequence of cubes in Z+ satisfying the \"cone-condition\". The identification of the limit is given. A moving local theorem is also proved.
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Citations
Convergence of moving averages of multiparameter superadditive processes.
Doğan Çömez
- 01 Jan 1998
TL;DR: In this article, it was shown that moving averages sequences are good in the mean for strongly superadditive processes in L1, and good in p-mean for multiparameter admissible superadditives in Lp, 1 ≤ p <∞.
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Multi–Parameter Moving Averages
Roger L. Jones,James Olsen +1 more
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TL;DR: In this article, the authors presented a dynamical system, (X, Σ,m,T), where X is a probability space and T is a measure preserving point transformation from X onto itself When T is induced by nonsingular point transformations, τx is written as Tx.
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On certain maximal functions and approach regions
Alexander Nagel,Elias M. Stein +1 more
TL;DR: In this paper, it was shown that there are many approach regions which are not contained in any nontangential region but for which the conclusions of Fatou's theorem remain true.