论文标题
Sard定理清晰度的基本例子
An elementary example of Sard's Theorem sharpness
论文作者
论文摘要
在本说明中，我们定义了$ c^1 $函数$ f：[0，m]^2 \ to [0,2] $，它满足其临界值的集合具有正值。此功能提供了一个示例，比通常在文献中出现的功能更容易，即如何改善Sard定理中所需的可怜性顺序
In this note we define a $C^1$ function $F:[0,M]^2\to [0,2]$ that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differentiability required in Sard's Theorem cannot be improved
