Generalized Lebesgue Spaces and Application to Statistics

Huaiyu Zhu

Working Papers from Santa Fe Institute

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.

Keywords: Lebesgue space; fractional powers of measures; completeness; duality; ideal estimates (search for similar items in EconPapers)
Date: 1998-06
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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:98-06-044

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