Absolute curvature measures for unions of sets with positive reach
Absolute curvature measures for unions of sets with positive reach
复制标题
具有正范围的集合并集的绝对曲率测量
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Rataj
中科院分区：
文献类型：
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作者：
J. Rataj
引入了正可达集的局部有限并的绝对曲率测度，通过考虑指标函数的绝对值，推广了Zahle [13]的定义.这一定义不同于Matheron [5]和Schneider [12]的定义。证明了绝对曲率测度的Crofton型交公式。通过一个例子说明了绝对曲率测度在几何统计中的作用。
Absolute curvature measures for locally finite unions of sets with positive reach are introduced, extending the definition of Zahle [13] by taking into account the absolute value of the index function. It is shown that this definition differs from that of Matheron [5] and Schneider [12]. An intersection formula of Crofton type for absolute curvature measures is proved. The role of absolute curvature measures in geometric statistics is illustrated by an example.