Definition 1.3.2 (Abstract Wiener Space).label Let $E$ be a separable Banach space over $\real$, $H \subset E$ be a Hilbert space over $\real$ that is continuously embedded into $E$, and $\wien: \cb(E) \to [0, 1]$ be a Gaussian measure, then the triple $(H, E, \wien)$ is an abstract Wiener space if
\[\wh \wien(x^{*}) = e^{-\norm{\iota^* x^*}_H^2/2}\quad \forall x^{*} \in E^{*}\]