Published in The American Mathematical Monthly, Volume 90, Issue 7, August 1, 1983, pages 438-442. Copyright © 1983 Mathematical Association of America. The definitive version is available at http://www.jstor.org/stable/2975720.
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.