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On equivalence of strong and weak convergence inL 1-spaces under extreme point conditions

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Abstract

Under suitable extreme point conditions weak convergence can imply strong convergence inL 1-spaces [28, 31, 12, 26] Here a number of such results are generalized by means of a unifying, very general approach using Young measures. The required results from Young measure theory are derived in a new fashion, based on pointwise averages [6], from well-known results on weak convergence of probability measures.

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Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

    Erik J. Balder

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  1. Erik J. Balder
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Dedicated to Lucien Le Cam, on the occasion of his 65th birthday

Research done at the Banach Mathematical Center, Warsaw; partly supported by NUFFIC, The Hague.

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Balder, E.J. On equivalence of strong and weak convergence inL 1-spaces under extreme point conditions. Israel J. Math. 75, 21–47 (1991). https://doi.org/10.1007/BF02787180

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  • DOI: https://doi.org/10.1007/BF02787180

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