Gaussian measures on Orlicz spaces and abstract Wiener spaces

Gaussian measures on some non-Banach spaces of measurable functions are investigated. The main result is that every Gaussian measure on a separable Orlicz space L[phi] is an extension of the canonical cylindrical Gaussian distribution on the RKHS. As an application we obtain some results concerning the support of Gaussian measures on L[phi] as well as the law of the iterated logarithm for sequences of i.i.d. Gaussian random elements with values in L[phi].