The Measure Representation: A Correction

Wakker [9] and Puppe [2] point out a mistake in Theorem 1 in Segal [6]. This theorem deals with representing preference relations over lotteries by the measure of their epigraphs. An error in the theorem is that it gives wrong conditions concerning the continuity of the measure. This paper corrects the error. Another problem is that the axioms do not imply that the measure is bounded, therefore the measure representation applies only to subsets of the space of lotteries, although these subsets can become arbitrarily close to the whole space of lotteries. Some additional axioms (Segal [6, 7]), implying that the measure is a product measure (and hence anticipated utility), also guarantee that the measure is bounded.