Firstly about the terminology of ‘infinite dimensional distributions’. The reason why the distributions to be treated in this chapter are called infinite dimensional is that the underlying spaces will be some Banach space, a topological vector space or the dual of a countably Hilbertian nuclear space unlike the distributions like \(\mathcal{D}' \) or \(\mathcal{S}'\) where the underlying space is usually the finite dimensional \(\mathbb {R}^{n}.\)