In *stochastic equations in infinite dimensions* written by Da Prato **reproducing kernel Hilbert space** is defined

Let $\mu$ be a symmetric Gaussian measures on a separable Banach space $E$. A linear subspace $H \subset E$ equipped with a Hilbert norm $|\cdot|_{H}$ is said to be a

reproducing kernel Hilbert spacefor $\mu$ if H is complete, continuously embedded in $E$ and such that for arbitrary $\varphi \in E^{\star}$, the distribution of $\varphi$ is Gaussian $\mathcal{N}(0,|\varphi|^2_{H})$, where $$|\varphi|_{H}=\sup_{|h|\leq 1, h\in H}|\varphi(h)|$$

My question is

(1) How can this definition coincide with the general definition such as

http://en.wikipedia.org/wiki/RKHS

(2) What is the advantage of this defination? Is there any convenience?