In this paper, we introduce two new types of conditional random set taking values in a Banach space: the conditional interior and the conditional closure. The conditional interior is a version of the conditional core, as introduced by A. Truffert and recently developed by Lepinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure is a generalization of the notion of conditional support of a random variable. These concepts are useful for applications in mathematical finance and conditional optimization.

中文翻译：

---

随机集的条件内部和条件闭包

在本文中，我们介绍了在 Banach 空间中取值的两种新型条件随机集：条件内部和条件闭包。条件内部是条件核的一个版本，由 A. Truffert 引入，最近由 Lepinette 和 Molchanov 开发，可以看作是拓扑内部的可测量版本。条件闭包是对随机变量的条件支持概念的概括。这些概念对于数学金融和条件优化中的应用非常有用。