We derive bounds for the Orlicz norm of the deviation of a random variable defined on $\mathbb{R}^n$ from its Gaussian mean value. The random variables are assumed to be smooth and the bound itself depends on the Orlicz norm of the gradient. Applications to non-parametric Information Geometry are discussed.

翻译：我们得出Orlicz 规范的界限, 以 $\mathbb{R ⁇ n$ 定义的随机变量偏离其高斯平均值。 随机变量假定是平滑的, 约束本身取决于梯度的 Orlicz 规范。 讨论对非参数信息几何的应用 。