Abstract

For a \(d\)-dimensional convex body we define new integral geometric concepts: conditional moments of the random chord length and conditional moments of the distance of two independent uniformly distributed points in the body. In addition, the relations between the concepts are found in this article.

中文翻译：

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$$\boldsymbol{d}$$ -Dimensional Convex Body 的条件矩

摘要

对于\(d\)维凸体，我们定义了新的积分几何概念：随机弦长的条件矩和体中两个独立均匀分布点的距离的条件矩。此外，本文还介绍了概念之间的关系。