  We obtain a representation theorem for Banach space valued Gaussian random
variables as integrals against a white noise. As a corollary we obtain
necessary and sufficient conditions for the existence of a white noise
representation for a Gaussian random field indexed by a compact measure space.
As an application we show how existing theory for integration with respect to
Gaussian processes indexed by $[0,1]$ can be extended to Gaussian fields
indexed by compact measure spaces.
