A proof of the equivalence of ensembles for asymptotically decoupled fields relying on Mosco's theorem

We give a proof of the identification between the entropy and the opposite of the Fenchel-Legendre transform of the pressure for asymptotically decoupled fields relying on Mosco's theorem. ----- Nous d\'emontrons l'identification entre l'entropie et l'oppos\'ee de la transform\'ee de Fenchel-Legendre de la pression pour les champs asymptotiquement d\'ecoupl\'es \`a partir du th\'eor\`eme de Mosco.