Optimal-partitioning inequalities for nonatomic probability measures
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- by John Elton, Theodore P. Hill and Robert P. Kertz PDF
- Trans. Amer. Math. Soc. 296 (1986), 703-725 Request permission
Abstract:
Suppose ${\mu _1}, \ldots ,{\mu _n}$ are nonatomic probability measures on the same measurable space $(S,\mathcal {B})$. Then there exists a measurable partition $\{ {S_i}\} _{i = 1}^n$ of $S$ such that ${\mu _i}({S_i}) \geq {(n + 1 - M)^{ - 1}}$ for all $i = 1, \ldots ,n$, where $M$ is the total mass of $\vee _{i = 1}^n {\mu _i}$ (the smallest measure majorizing each ${\mu _i}$). This inequality is the best possible for the functional $M$, and sharpens and quantifies a well-known cake-cutting theorem of Urbanik and of Dubins and Spanier. Applications are made to ${L_1}$-functions, discrete allocation problems, statistical decision theory, and a dual problem.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 296 (1986), 703-725
- MSC: Primary 60A10; Secondary 28A99, 60E15
- DOI: https://doi.org/10.1090/S0002-9947-1986-0846603-9
- MathSciNet review: 846603