In various stereological problems an $n$-dimensional convex body is intersected with an $(n-1)$-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the $(n-1)$-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions.

翻译：在多种体视学问题中，一个$n$维凸体与一个$(n-1)$维各向同性均匀随机超平面相交。本文研究了此类随机截面所对应的$(n-1)$维体积的累积分布函数。该分布分别在平面和空间情形下被称为弦长分布和截面面积分布。针对多类凸体，证明了这些分布函数关于勒贝格测度是绝对连续的。提出了一种蒙特卡洛模拟方法用于逼近相应的概率密度函数。