COMPETITIVE EQUILIBRIUM WITH AN ATOMLESS MEASURE SPACE OF AGENTS AND INFINITE DIMENSIONAL COMMODITY SPACES WITHOUT CONVEX AND COMPLETE PREFERENCES

We prove the existence of a competitive equilibrium for an economy with an atomless measure space of agents and an infinite dimensional commodity space. The commodity space is a separable Banach space with a non-empty interior in its positive cone. We dispense with convexity and completeness assumptions on preferences. We employ a saturated probability space for the space of agents which enables us to utilize the convexifying effect on aggregation. By applying the Gale-Nikaido-Debreulemma, we provide a direct proof of the existence of a competitive equilibrium.