A proportionality principle for partitioning problems

Hill, Theodore P.

doi:10.1090/S0002-9939-1988-0938685-8

A proportionality principle for partitioning problems
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by Theodore P. Hill

Proc. Amer. Math. Soc. 103 (1988), 288-293

DOI: https://doi.org/10.1090/S0002-9939-1988-0938685-8

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Abstract:

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.

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