Determinateness of the Utility Function: Revisiting a Controversy of the Thirties
重新审视了三十年代关于效用函数基数性的争论，指出其结论依赖于分析框架：在无限制域假设下成立，但在现代选择理论中，仅当效用函数连续且定义在连通拓扑空间上时才成立。
It has been alleged that, contrary to the assumptions in Pareto's Manual, the ability to compare first-differences of utility implies cardinality. It is shown here that the validity of this theorem hinges critically on the framework of analysis. In the framework of the thirties it is valid because of the implicit use of an ‘unrestricted domain’ assumption. In the modern choice-theoretic context it is not in general true but it becomes valid if utility functions are continuous and are defined on a connected topological space.