In a recent international conference on Game Theory，Professor Shapley presented a new bargaining set concept，which avoid bargaining among players，and so can be generalized to the games with infinitely many players. In this paper，the new bargaining set for continuous convex games is proved to be coincided with the core，thus the main results of [1] and [2] may be generalized to a great extent. As a by-product of our proof，a new generalization of Hahn decomposition theorem in measure theory is obtained.