与L^P空间相关的Banach空间L~ψ

The Banach SpaceL L￣ψ Relative to the Spaces L￣p

设Ｘ是局部紧距离空间，而μ是Ｘ上的全有限非负Ｂｏｒｅｌ测度。又设ψ（ｔ）是定义在［１，＋∞）上取正值的函数且使得．在范数线性赋范空间是完备可分的。而且对Ｌ￣ψ（ｘ）上的任一有界线性泛函Φ，存在唯一的函数Ｆ∈Ｌ￣１（Ｘ）使得。

Let X be a locally compact metric space,μa totally finite non-negative Borelmeasure on X,Let ψ> be a function [1,+∞)with The author proves that thelinear normed space is complete and separable in the Furthermore , for each bounded linear functional Φ onL￣ψ(X) there exists unique function F∈L￣1(X) such that。