  We prove in this article that every Borelian measure, for example, the
distribution of a random variable, in separable Banach space has a support
which is compact embedded Banach subspace; and prove that if the norm of the
random variable belongs to some exponential Orlicz space, then the new subspace
can be choose such that the norm of this variable in the new space also belongs
to other exponential Orlicz space.
