Gaussian measures on Orlicz spaces

Abstract

Gaussian measures on some spaces of measurable functions, which are not necessarily Banach spaces are investigated . The main result is that every centered Gaussian measure on a separable Orlicz space Lф (such that ) is equivalent to ф( t ) concave is the image under a continuous linear map o f a centered Gaussian measure on a separable, real Hilbert space. As an application we obtain the CLT and the LIL