2 APPLICATIONS OF A THEOREM OF DVORETSKY, WALD, AND WOLFOVITZ TO CAKEDIVISION

In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any seq uence of positive real numbers that sum to one (which may be thought o f as representing the players' relative entitlements), we show that th ere exists a partition in which each player receives either more than, less than, or exactly his or her entitlement (according to his or her measure), in any desired combination, provided that the measures are not all equal.