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Generalized Lebesgue Spaces and Application to Statistics

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  • Huaiyu Zhu
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    Abstract

    Statistics requires consideration of the ``ideal estimates'' defined through the posterior mean of fractional powers of finite measures. In this paper we study , the linear space spanned by th power of finite measures, . It is shown that generalizes the Lebesgue function space , and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach space with as its dual. These results are analogous to classical counterparts but do not require a dominating measure. They also guarantee the unique existence of the ideal estimate.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 98-06-044.

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    Date of creation: Jun 1998
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    Handle: RePEc:wop:safiwp:98-06-044

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    Related research

    Keywords: Lebesgue space; fractional powers of measures; completeness; duality; ideal estimates;

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