论文标题
具有应用的不可分割的Banach空间上的积分功能
Integral functionals on nonseparable Banach spaces with applications
论文作者
论文摘要
在本文中，我们研究了在函数空间上定义的积分函数，该功能具有一般（不可分割的）Banach空间的值。我们介绍了一类新的集成和多种功能，为此我们获得了可测量的选择结果。然后，我们在集成和iNVimum之间提供一个互换公式，这使我们能够为整体函数的共轭和Clarke细分获得明确的公式。从随机编程中的预期功能，给出了变异问题的计算和扫描过程的最佳条件。
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results. Then, we provide an interchange formula between integration and infimum, which enables us to get explicit formulas for the conjugate and Clarke subdifferential of integral functionals. Applications to expected functionals from stochastic programming, optimality conditions for a calculus of variation problem and sweeping processes are given.
