Generalized Lebesgue Spaces and Application to Statistics
نویسنده
چکیده
Statistics requires consideration of the “ideal estimates” defined through the posterior mean of fractional powers of finite measures. In this paper we study L1= , the linear space spanned by th power of finite measures, 2 (0; 1). It is shown that L1= generalizes the Lebesgue function space L1= ( ), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach space with L1=(1 ) 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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