Abstract
It is proved that a (not necessarily dominated) family of probability measures is boundedly complete iff the closed linear hull of this family in the weak star topology coincides with the set of all finite and signed measures, which are continuous with respect to this family. In the dominated case this characterization reduces to a well known result. As an application it is shown that bounded completeness is preserved with respect to families of product probability measures without any additional assumptions.
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References
N. Dunford, T. J. Schwartz: Linear Operators. Part I. Interscience Publishers, New York 1964.
D. A. S. Fraser: Nonparametric Methods in Statistics. Wiley, New York 1957.
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Plachky, D. (1977). A Characterization of Bounded Completeness in the Undominated Case. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_48
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DOI: https://doi.org/10.1007/978-94-010-9910-3_48
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9912-7
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