Published in Proceedings of the American Mathematical Society, Volume 108, Issue 1, May 1, 1988, pages 288-293. Copyright © 1988 American Mathematical Society. The definitive version is available at http://dx.doi.org/10.1090/S0002-9939-1988-0938685-8.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
In a general class of measure-partitioning or fair-division problems, the extremal case occurs when the measures are proportional. Applications are given to classical and recent fair-division problems, and to statistical decision theory, mathematical physics, Banach space theory, and inequalities for continuous random variables.