摘要：{Abstract } In 1954 Debreu wrote a classic paper in which he considered the problem of representing preferences by utility functions. The idea was to assign numbers (or utilities) to commodities in such a way that if commodity x is less preferred than y then the utility of y must be greater than the utility of x. Debreu showed that not all preference orderings can be represented by utility functions. He then stated and proved two fundamental theorems which specified the precise conditions under which preferences can be given a utility representation. In this paper Debreu worked with complete preference orderings i.e. orderings in which any two commodities are comparable. In 1970 Peleg proved a theorem in Econometrica for partial preference orderings, i.e. orderings in which it is not necessarily true that all commodities are comparable. In 1971 Lee wrote a paper in which he suggested that Debreu's theorems can be deduced from Peleg's theorem.
