On the Uniqueness of Individual Demand at Almost Every Price System

The fact that even in case of a nonconvex preference relation the demand set is a singleton at almost every budget situation has been proved by Mas-Cole11 [2] and by Mas-Cole11 and Neuefeind [3]. Mas-Colell’s proof made use of the theory of Hausdorff measures on lower dimensional subspaces of a Euclidian space. The proof due to Mas-Cole11 and Neuefeind relies on an application of the projection theorem for analytic sets due to Marczewski and Ryll-Nardzewski [l] together with Fubini’s theorem. In the present note I shall give a new proof which relies only on the disintegration theorem (cf. Parthasarathy, [4, Theorem 8.1, p. 1471). i.e., a general version of Fubini’s theorem.