# Utility representation theorems for Debreu separable preorders

Published on May 1, 2012in Journal of Mathematical Economics0.634

· DOI :10.1016/j.jmateco.2012.02.005

Abstract

We prove the existence of arbitrary (resp., semicontinuous, continuous) utility representations for arbitrary (resp., semicontinuous, continuous) preorders satisfying some weakened Debreu order separability conditions. In this way we widely generalize a classical result for total preorders that essentially is due to Debreu.