How McFadden met Rockafellar and learned to do more with less
利用凸分析工具，在无分布和函数形式限制下，推广了离散选择中的威廉姆斯-戴利-扎卡里定理和霍茨-米勒需求反演定理，给出了需求及其反函数简化为函数的充要条件。
We exploit the power of convex analysis to synthesize and extend a range of important results concerning the additive random utility model of discrete choice. With no restrictions on the joint distribution of random utility components or the functional form of systematic utility components, we formulate general versions of the Williams–Daly–Zachary theorem for demand and the Hotz–Miller demand inversion theorem. Based on these theorems, we provide necessary and sufficient conditions for demand and its inverse to reduce to functions. These conditions jointly imply that demand is a continuous function with a continuous inverse.