We study the properties of multivalued mappings of general form with respect to the possibility of finding their nonanticipating selections. The property of nonanticipation is formulated for an arbitrary domain by specifying some family of “test” subsets. Sufficient conditions for the existence of a nonanticipating selection of a nonanticipating multivalued mapping are proposed: the values of the mapping must be nonempty compact sets, and the family of “test” subsets must be totally ordered with respect to inclusion. We illustrate the results by showing their applicability to the pursuit–evasion differential game in the form of P. Varaya and J. Lin.

中文翻译：

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关于多值映射的非预期选择的构造

我们针对发现其非预期选择的可能性来研究一般形式的多值映射的属性。通过指定一些“测试”子集族，可以为任意域制定非预期属性。提出了用于非预期多值映射的非预期选择的充分条件：映射的值必须为非空紧集，并且“测试”子集族必须相对于包含被完全排序。我们通过以P. Varaya和J. Lin的形式展示其对追击-逃避微分游戏的适用性来说明结果。