Martingales,the smoothing index and ergodic theory |
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Authors: | Louis H. Blake |
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Affiliation: | Faculty of Pure and Applied Sciences, Richmond College, City University of New York, Staten Island, NY 10301, U.S.A. |
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Abstract: | A classical theorem of Meyer Jerison which shows that the convergence in the pointwise ergodic theorem is equivalent to the convergence of an associated martingale is expanded to a conditional setting. An equiconvergence theorem of the type established for martingales by N.F.G. Martin and E. Boylan is established in the ergodic case for an ergodic, non-invertible, measure-preserving transformation. |
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Keywords: | martingales ergodic theory |
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