is unfortunately a typographical slip at a key point which may confuse So it will be sketched here for convenience. As a consequence one obtains that the space of pre-Gaussian variables g is a

In the problems of large deviations of BM and the general Gaussian processes, it was seen that the Fenchel-Young function L : c R+ where c is an infinite dimensional Polish space, and in the preceding section the classical Young functions leading to exponential Orlicz spaces. These two facts motivate the following functional analysis study. Thus L must be convex but not necessarily symmetric and not bounded, i.e., L(tx) ¥ as t ¥ for each 0 ¹ x Î c . Simple examples show that even when c = IR2 the last condition need not hold for a convex L, and has to be assumed. In this extension, even if L(–x) = L(x), i.e., symmetric, its conjugate L need not be. A first step in this direction may be formulated as follows.