Abstract
We consider a positive distribution H such that H defines a probability measure k=k H on the dual of some real nuclear FrEchet space. A large deviation principle is proved for the family {k n ,n.1} where k n denotes the image measure of the product measure k H n under the empirical distribution function L n . Here the rate function I is defined on the space F (N)+ and agrees with the relative entropy function $\widetilde{H}(\Psi/\Phi)$ . As an application, we cite the Gibbs conditioning principle which describes the limiting behaviour as n tends to infinity of the law of k tagged particles Y 1,...,Y k under the constraint that L n Y belongs to some subset A 0.