Abstract
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 φ 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 φ as well as the law of the iterated logarithm for sequences of i.i.d. Gaussian random elements with values in L φ .
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