  We prove a linear version of Dawson-G{\"a}rtner theorem: weak large deviation
principles and the equality --s = p* between the negentropy and the
Fenchel-Legendre transform of the pressure are preserved through linear
projective limits. As a result, the equality --s = p* holds in great generality
for empirical means of independent and identically distributed random variables
(Cram{\'e}r's theory), e.g. in any measurable normed space, and even in any
projective limit of such spaces. Eventually, we give an original example where
--s is different from p* and discuss the dual equality.
