论文标题
衡量理论的完成程序
Completion procedures in measure theory
论文作者
论文摘要
我们通过添加新的无效集合，提出了对组价值内容物的扩展（即定义在环上定义的加性集功能）的统一处理。我们的方法基于内容$μ$的完成戒指的概念。每种这样的戒指$ \ Mathcal n $，$μ$的扩展是自然关联的，称为$ \ Mathcal n $ completion $μ$。 $ \ Mathcal n $ completion操作包括最初已知的完成型过程，还引起了一些新的扩展，这对于在测量理论中构建反例可能很有用。我们发现一种条件，确保了内容的$σ$ - 添加性能在$ \ Mathcal n $ completion下保留，并为$ \ Mathcal n $ completion建立标准，以再次成为一种措施。
We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content $μ$. With every such ring $\mathcal N$, an extension of $μ$ is naturally associated which is called the $\mathcal N$-completion of $μ$. The $\mathcal N$-completion operation comprises most previously known completion-type procedures and also gives rise to some new extensions, which may be useful for constructing counterexamples in measure theory. We find a condition ensuring that $σ$-additivity of a content is preserved under the $\mathcal N$-completion and establish a criterion for the $\mathcal N$-completion of a measure to be again a measure.
