  We prove a generalisation of Fernique's theorem which applies to a class of
(measurable) functionals on abstract Wiener spaces by using the isoperimetric
inequality. Our motivation comes from rough path theory where one deals with
iterated integrals of Gaussian processes (which are generically not Gaussian).
Gaussian integrability with explicitly given constants for variation and
H\"older norms of the (fractional) Brownian rough path, Gaussian rough paths
and the Banach space valued Wiener process enhanced with its L\'evy area
[Ledoux, Lyons, Quian. "L\'evy area of Wiener processes in Banach spaces". Ann.
Probab., 30(2):546--578, 2002] then all follow from applying our main theorem.
