Generalized Lebesgue Spaces and Application to Statistics
AbstractStatistics 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 InfoPaper provided by Santa Fe Institute in its series Working Papers with number 98-06-044.
Date of creation: Jun 1998
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Lebesgue space; fractional powers of measures; completeness; duality; ideal estimates;
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