Proof. Let $\seq{x_n^*}\subset E^{*}$ such that $\seq{\iota^* x_n^*}$ is an orthonormal basis for $H$. For each $n \in \nat$, let $X_{n}(x) = \dpb{x, x_n^*}{E}$, then $\seq{X_n}$ is a family of independent Gaussian random variables with variance $1$. Thus $\sum_{n \in \nat}X_{n}^{2} = \infty$ almost surely. By (2) of Lemma 1.3.1, $\wien(H) = 0$.$\square$