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Full-Text Articles in Physical Sciences and Mathematics
Prophet Inequalities For Averages Of Independent Non-Negative Random Variables, Theodore P. Hill
Prophet Inequalities For Averages Of Independent Non-Negative Random Variables, Theodore P. Hill
Research Scholars in Residence
No abstract provided.
Optimal-Partitioning Inequalities For Nonatomic Probability Measures, John Elton, Theodore P. Hill, Robert P. Kertz
Optimal-Partitioning Inequalities For Nonatomic Probability Measures, John Elton, Theodore P. Hill, Robert P. Kertz
Research Scholars in Residence
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, …