给出高斯迷向凸体和高斯迷向常数的定义,证明高斯迷向凸体的存在性和正交不变性等.另外,通过对单位体积球体和方体的高斯迷向常数进行计算,发现其具有与Lebesgue测度下凸体迷向常数变化相反的性质.

Gaussian isotropic bodies and Gaussian isotropic constants were defined, and the existence and orthogonal invariability of Gaussian isotropic bodies were proved. By calculating the Gaussian isotropic constants of a ball and a cube, both with unit volume, we show that changes in the Gaussian isotropic constants in the Gaussian measure are opposite to those in the Lebesgue measure.