We present some results concerning the links between the set of walrasian equilibrium points W(E) and the core C(E) of an economy E with infinite dimensional space of agents and commodities where E = [(T; ¿; ¹);E; (X;>t); e] ([1]). The following hypothesis will be considered.(H0) The submeasure ¹ satisfies the following condition: (9) fEi; i = 1; rg a partition of T such that, for every A 2 A, ¹(A) = Xr i=1 ¹(A \ Ei): (Ei denotes the set of agents of type i). (H1) Each consumer a 2 Ei is characterized by its initial endowment e(a) = ei: (H2) The preference relation f>igi=1;r associated to the agents a 2 Ei is (i) irreflexive and transitive, (ii) monotone: 8x 2 E+; v 2 E+ n f0g; x + v >i x; 8i · r, (iii) continuous: the set fy 2 E+; y ¸i xg is closed in E, 8i · r. In other words, in each coalition Ei agents share the same initial endowment and same preference criterions. (H3) The price system is P = conv cone G, where G is a family of functions G ½ F(E;R+) with the following properties: (i) g(0) = 0; 8g 2 G, (ii) g(c) · g(d); 8g 2 G =) c < d, (iii) d ¡ c 2 E+ n f0g =) g(c) < g(d); 8g 2 G n f0g. (H4) The aggregate operator A(f; ¹) = (G) R f d¹, where the G-integral is given by g((G) Z f d¹) = (Ch) Z g ± f d¹; 8g 2 G: Theorem. Under assumptions (H0) ¡ (H4), we have W(E) ½ C(E).