分離原理及其應用

Abstract

此論文研究一個可推得Hahn-Banach等相關定理的分離原理的等價定理。由此，我們為Agnew-Morse定理、交換群上的順從性、Haar integral的存在性提供自然簡潔的證明。可想像的是這個方法也能幫助分析上其他相關的結果。

This thesis studies an analytic variant of a well-known separation principle from which follows Hahn-Banach theorem and many basic theorems in convex analysis. By using this analytic variant, we provide natural and elegant proofs for Agnew-Morse Theorem, the amenability of abelian groups, and the existence of Haar integrals. It is conceivable that the approach we suggest here might lead to clarification of some results in convex analysis.