Inequalities for α-Optimal Partitioning of a Measurable Space

DOI10.2307/2047621zbMath0693.60004OpenAlexW4254668497MaRDI QIDQ3468364

Jerzy Legut

Publication date: 1988

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2047621

zbMATH Keywords

optimal partitioningmeasurable partitionsnonatomic probability measures

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Minimax procedures in statistical decision theory (62C20) Probabilistic measure theory (60A10) Classical measure theory (28A99)

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A sharp partitioning-inequality for non-atomic probability measures based on the mass of the infimum of the measures ⋮ Maximin share and minimax envy in fair-division problems. ⋮ How to obtain a range of a nonatomic vector measure in \(\mathbb R^2\) ⋮ On totally balanced games arising from cooperation in fair division ⋮ Finding maxmin allocations in cooperative and competitive fair division ⋮ The Dubins-Spanier optimization problem in fair division theory ⋮ Bounds for \(\alpha\)-optimal partitioning of a measurable space based on several efficient partitions ⋮ How to obtain an equitable optimal fair division ⋮ Optimal Fair Division for Measures with Piecewise Linear Density Functions ⋮ Minimax risk inequalities for the location parameter classification problem ⋮ Optimal partitioning of a measurable space into countably many sets ⋮ Optimal Partitioning of a Measurable Space ⋮ A sharp nonconvexity bound for partition ranges of vector measures with atoms

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