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We prove a convergence property for some families of finely harmonicfunctions on a fine domain $U$ of $\RR^n$ ($n\ge 2$), and we apply it to provesome regularity of the fine Green kernel of $U$.

Propri\'et\'e de convergence de certaines familles de fonctions finement harmoniques et r\'egularit\'e du noyau de Green d'un domaine fin