The purpose of this paper is investigating various solutions of continuous convex games with contably many players. We showed that for such games,the core is the unique stable set and coincides with the bargaininng set (for the grand coalition)，and the kernel (for the grand coalition)is a nonempty subset of the core. These can be viewed as a generalization of similar results obtained by Shapley，Maschler and Peleg. The values of the games are also considered and it is proved that the Banach space acM，introduced by Artstein，is the closed linear subspace generated by all these games. Moreover，the value of every such game is in the core，as is the case for finite convex games.