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Characterization of some types of completeness resp. Total completeness and their conservation under direct products

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Abstract

Some notions ofL p (μ)-completeness resp. totally L p (μ)-completeness (1≦p≦∞) are characterized for families of probability distributions dominated by aσ-finite measureμ and their conservation with respect to direct products is proved. Furthermore, it is shown that totallyL ∞(μ)-completeness does not implyL 1(μ)-completeness and that there are families of probability distributions in the i.i.d. case induced by the order statistic, which are L1(μ)-complete but not totallyL ∞(μ)-complete.

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Authors and Affiliations

  1. Institute of Math. Statistics, University of Münster, Einsteinstraße 62, D-4400, Münster

    D. Plachky

  2. Department of Mathematics and Statistics, University of Maryland at Baltimore County, 21228, Baltimore, MD, USA

    A. L. Rukhin

Authors
  1. D. Plachky
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  2. A. L. Rukhin
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Plachky, D., Rukhin, A.L. Characterization of some types of completeness resp. Total completeness and their conservation under direct products. Metrika 38, 369–376 (1991). https://doi.org/10.1007/BF02613635

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  • DOI: https://doi.org/10.1007/BF02613635

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