对偶对条件扩张的向量对偶
Vector duality via conditional extension of dual pairs
摘要：
建立了真凸下半连续函数$f\colon X\to \overline{L^0}$的Fenchel-Moreau型对偶，其中$(X,Y,\langle \cdot,\cdot \rangle)$是巴拿赫空间的对偶对，$\overline{L^0}$是所有扩展实值可测函数的集合.我们提供了下半连续的概念，这是等价于存在的一个对偶表示的元素在Bochner空间$L^0(Y)$。为了得到对偶结果，构造了几个条件完备化和扩张。这是arXiv e-print 1708.03127的早期版本，其中主要结果是在条件完成，条件扩展和条件实数的抽象设置中制定的。
英文摘要：
A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\colon X\to \overline{L^0}$ is established where $(X,Y,\langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\overline{L^0}$ is the set of all extended real-valued measurable functions. We provide a concept of lower semi-continuity which is shown to be equivalent to the existence of a dual representation in terms of elements in the Bochner space $L^0(Y)$. To derive the duality result, several conditional completions and extensions are constructed. This is an earlier version of arXiv e-print 1708.03127, where the main results were formulated in an abstract setting of conditional completions, conditional extensions and conditional real numbers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
