Utility representation theorems for Debreu separable preorders

作者：Herden Gerhard; Levin Vladimir L^*

来源：Journal of Mathematical Economics, 2012, 48(3): 148-154.

DOI：10.1016/j.jmateco.2012.02.005

• Debreu separability
• Weak Debreu separability
• Topological space
• Continuous preorder
• Utility function
• Open decreasing set
• Separable system

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.