Let $${\eta}=\left({\eta_j}\right)$$ be a sequence of independent Gaussian, means 0, Varriance 1, random variable in all of this paper. We shall then study the distribution of $$q\left( {\eta}\right)\quad {\rm or} \quad q\left({\eta- a}\right)$$ where $$q: {\mathbb{R}}^{\infty}\rightarrow {\mathbb{\bar{R}}}_+=\left[0,\infty\right]$$ is a seminorm and a $$\in \mathbb{R^{\infty}}.$$ In particular we shall study the behavior of $$P\left(q{\left({\eta}\right)}\,{\leq}\, {t}\right)\quad {\rm as} \quad {t}\,{\rightarrow \, 0}.$$