Characterization of some types of completeness resp. Total completeness and their conservation under direct products |
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| Authors: | D Plachky A L Rukhin |
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| Institution: | 1. Institute of Math. Statistics, University of Münster, Einsteinstra?e 62, D-4400, Münster
2. Department of Mathematics and Statistics, University of Maryland at Baltimore County, 21228, Baltimore, MD, USA
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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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| Keywords: | |
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