Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space
Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space
复制标题
DOI：
10.1016/j.jmaa.2011.11.025
复制
发表时间：
2011-07
期刊：
影响因子：
--
通讯作者：
T. Guo;Yujie Yang
中科院分区：
文献类型：
--
作者：
T. Guo;Yujie Yang
在最近关于条件风险测度的研究工作的启发下，本文研究了L¯0值函数的Ekeland变分原理，其中L¯0是概率空间上扩展实值随机变量等价类的集合。首先，我们证明了定义在完全随机度量空间上的函数的Ekeland变分原理的一般形式。然后，对完全随机赋范模上的局部函数给出了更精确的Ekeland变分原理。最后，作为应用，我们在随机共轭空间框架下建立了完全随机赋范模上的Bishop-Phelps定理。
Motivated by the recent work on conditional risk measures, this paper studies the Ekelandʼs variational principle for a proper, lower semicontinuous and lower bounded L¯0-valued function, where L¯0is the set of equivalence classes of extended real-valued random variables on a probability space. First, we prove a general form of Ekelandʼs variational principle for such a function defined on a complete random metric space. Then, we give a more precise form of Ekelandʼs variational principle for such a local function on a complete random normed module. Finally, as applications, we establish the Bishop–Phelps theorem in a complete random normed module under the framework of random conjugate spaces.