测度与积分理论中的扩张定理作为完备性公理

中文摘要 AI 辅助

在测度与积分理论中，将预测度扩张为外测度以及将Daniell线性泛函扩张为Daniell积分的主题，由Caratheodory和Daniell的基础扩张定理所支配。这些定理被证明等价于Littlewood三原则，而后者已知是有序域完备性公理的等价替代形式。因此，测度与积分理论中的连续性定理也被纳入等价性列表之中。

英文摘要

In measure and integration theory, the themes of extending premeasures to outer measures and extending Daniell linear functionals to Daniell integrals are governed by the foundational extension theorems of Caratheodory and Daniell. These are proven to be equivalent to Littlewood's Three Principles, which are known to be equivalent alternatives to a completeness axiom for an ordered field. The continuity theorems of measure and integration theory are consequently shown to be included in the list of equivalences.

发表机构

• De La Salle University（德拉萨大学）

机构由 AI 辅助整理，请以论文原文为准。