Incompatibility of usual conditions for equilibrium existence in continuumeconomies without ordered preferences

In recent years attempts were made to extend the equilibrium existence resu lts of Gale and Mas-Colell (1975. J.Math. Econ. 2, 9-15) and Shafer and Son nenschein (1975, J. Math. Econ. 2, 345-348) to continuum economies. Here it is shown that the usual conditions used for these attempts force the "pref erred to" correspondence to be empty-valued almost everywhere on the nonato mic part of the measure space of agents. Several published continuum extens ions of the existence results of Shafer and Sonncnschein are thus rendered pointless. Journal of Economic Literature Classification Number: C72. (C) 2 000 Academic Press.