It was observed in [1] that the expectation of a squared scalar product of two random independent unit vectors that are uniformly distributed on the unit sphere in $R^n $ is equal to $1/n$. It is shown in this paper, that this is a characteristic property of random vectors defined on invariant probability subspaces of unit spheres in irreducible real representations of compact Lie groups.

翻译：[1]中观察到,两个随机独立单位矢量的平方弧弧产物以美元统一分布在单位域,等于1美元/n美元。 本文显示,这是随机矢量的特性,根据单位域的不定概率子空间来界定,不可复制地真实代表紧凑的“目标”组。