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Optimal-Partitioning Inequalities for Nonatomic Probability Measures
Transactions of the American Mathematical Society
  • John Elton, Georgia Institute of Technology - Main Campus
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
  • Robert P. Kertz, Georgia Institute of Technology - Main Campus
Publication Date
8-1-1986
Abstract
Suppose μ1,...,μn are nonatomic probability measures on the same measurable space (S, B). Then there exists a measurable partition {Si}ni=1 of S such that μi(Si) ≥ (n + 1 - M)-1 for all i = 1,...,n, where M is the total mass of Vni=1μ1 (the smallest measure majorizing each μi). 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 L1-functions, discrete allocation problems, statistical decision theory, and a dual problem.
Disciplines
Citation Information
John Elton, Theodore P. Hill and Robert P. Kertz. "Optimal-Partitioning Inequalities for Nonatomic Probability Measures" Transactions of the American Mathematical Society Vol. 296 Iss. 2 (1986) p. 703 - 725
Available at: http://works.bepress.com/tphill/41/