Definition 1.2.1.label Let $E$ be a separable Banach space over $\real$ and $\wien$ be a Borel measure on $E$, then $\wien$ is a Gaussian measure if $x \mapsto \angles{x, x^*}_{E}$ is a centred Gaussian random variable for each $x^{*} \in E^{*}$. If each $x \mapsto \angles{x, x^*}_{E}$ is non-degenerate, then $\wien$ is non-degenerate.