Published in Stochastic Inequalitites, Volume 22, January 1, 1993, pages 116-132. Copyright © 1993 Institute of Mathematical Statistics. The definitive version is available at http://dx.doi.org/10.1214/lnms/1215461947.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
This article surveys fair-division or cake-cutting inequalities in probability statistics, including bisection inequalities, basic fairness inequalities, convexity tools, superfairness inequalities, and partitioning inequalities hypotheses testing and optimal stopping theory. The emphasis is measure theoretic, as opposed to game theoretic or economic, and a number of open problems in the area are mentioned.