A linear version of Dawson-G\"artner's theorem

We prove a linear version of Dawson-G"artner’s theorem saying that weak large deviations principles and the equivalence of ensembles are preserved through linear projective limits.

Nous d'emontrons une version lin'eaire du th'eor`eme de Dawson-G"artner assurant que les principes de grandes d'eviations faibles et l’'equivalence d’ensemble sont conserv'es par passage aux limites projectives d’espaces vectoriels.