A constructive view on ergodic theorems

B.A.W. Spitters

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    2 Citaten (Scopus)

    Samenvatting

    Let T be a positive L1-L8 contraction. We prove that the following statements are equivalent in constructive mathematics. (1) The projection in L2 on the space of invariant functions exists: (2) The sequence (Tn)n¿N Cesáro-converges in the L2 norm: (3) The sequence (Tn)n¿N Cesáro-converges almost everywhere. Thus, we find necessary and sufficient conditions for the Mean Ergodic Theorem and the Dunford-Schwartz Pointwise Ergodic Theorem. As a corollary we obtain a constructive ergodic theorem for ergodic measure-preserving transformations. This answers a question posed by Bishop.
    Originele taal-2Engels
    Pagina's (van-tot)611-623
    Aantal pagina's13
    TijdschriftJournal of Symbolic Logic
    Volume71
    Nummer van het tijdschrift2
    DOI's
    StatusGepubliceerd - 2006

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