完备测度空间上可测函数的积分

Integral of Measurable Functions on Complete Measurable Spaces

一般测度空间(Ω,F,μ)已经有了其上可测函数的积分.在此基础上,把测度空间(Ω,F,μ)完备化而成为它的完备测度空间(Ω,F,μ),找到二者的关系.然后,给出完备测度空间上的可测函数积分的一种定义.且它与测度空间(Ω,F,μ)上的可测函数的积分是一致的.

Integral of measurable functions is defined on the common measurable space （Ω,F,μ）. On this basis,the measurable space （Ω,F,μ） is completed with respect to measurable space （Ω,^-F,^-μ） ,and the relations between them is found. Then, the integral of measurable functions on the complete measurable space （Ω,^-F,^-μ） is defined. It is also consistent with that on measurable space （Ω,F,μ） .