简单函数空间的完备化

The Completion of the Space of Simple Functions

在相当一般的测度空间(Ω,(?),μ)上,对于取值于Banach空间B的简单函数空间φ(Ω,μ,B),利用赋范线性空间完备化的方法,得到了L^p(Ω,μ,B)空间的理论(p≥1).这相应地推广了[2]的工作.

For very general measurable space (ΩDμ), the theory of Lp(ΩμB) (p≥1) is given for the space of simple functions φ(ΩμB), whose values are in the Banach space B. The results are generalizations of relative works in [2].