论文标题
将Rademacher定理扩展到设置值
Extending Rademacher Theorem to Set-Valued Maps
论文作者
论文摘要
Rademacher定理断言，Lipschitz在欧几里得空间之间的连续函数几乎在任何地方都可以区分。在这项工作中，我们将此结果扩展到了设置值的图，使用与凸流相关的设置可不同性的概念。我们的方法使用Rademacher定理，但也将其恢复为特殊情况。
Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability relating to convex processes. Our approach uses Rademacher theorem but also recovers it as a special case.
