可测空间的算子扩张及其上的等价关系

The spanning space of measurable space and the equivalence relation

讨论可测空间 (U,σ(U) )的两种不同的扩张 ,使其满足任意并 (交 )的封闭性 ,并证明二者是等价的 ,找到了利用可测空间 (U,σ(U) )的算子扩张空间 (U,σ* (U) )中的上 (下 )

Two kinds of spanning space of measurable space (U,σ(U)) are discussed so as to satisfying A t∈σ *(U)(t∈T),∪t∈TA t∈σ *(U)(∩t∈TA t∈σ *(U)). It has been proved that one was equivalent to the other. There exists a equivalence relation defined by upper (lower) approximate operator in the spanning space of measurable space (U,σ(U)).