  In this article, we show that every centered Gaussian measure on an infinite
dimensional separable Fr\'{e}chet space $X$ over $\mathbb R$ admits some full
measure Banach intermediate space between $X$ and its Cameron-Martin space. We
provide a way of generating such spaces and, by showing a partial converse,
give a characterization of Banach intermediate spaces. Finally, we show an
example of constructing an $\alpha$-H\"older intermediate space in the space of
continuous functions, $\mathcal C_0[0, 1]$ with the classical Wiener measure.
