We provide a two-sided inequality for the α-optimal partition value of a measurable space according to a finite number of nonatomic finite measures. The result extends and often improves Legut [Inequalities for α-optimal partitioning of a measurable space, Proc. Amer. Math. Soc. 104 (1988)] since the bounds are obtained considering several partitions that maximize the weighted sum of the partition values with varying weights, instead of a single one. Furthermore, we show conditions that make these bounds sharper.

Bounds for α-optimal partitioning of a measurable space based on several efficient partitions / Dall'Aglio, Marco; DI LUCA, Camilla. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 425:2(2015), pp. 854-863. [doi:10.1016/j.jmaa.2014.12.056]

Bounds for α-optimal partitioning of a measurable space based on several efficient partitions

DALL'AGLIO, MARCO;DI LUCA, CAMILLA
2015

Abstract

We provide a two-sided inequality for the α-optimal partition value of a measurable space according to a finite number of nonatomic finite measures. The result extends and often improves Legut [Inequalities for α-optimal partitioning of a measurable space, Proc. Amer. Math. Soc. 104 (1988)] since the bounds are obtained considering several partitions that maximize the weighted sum of the partition values with varying weights, instead of a single one. Furthermore, we show conditions that make these bounds sharper.
Dvoretzky–Wald–Wolfowitz convexity theorem Cake-cutting problems Fair division Optimal partitioning Convex analysis Maxmin solution
Bounds for α-optimal partitioning of a measurable space based on several efficient partitions / Dall'Aglio, Marco; DI LUCA, Camilla. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 425:2(2015), pp. 854-863. [doi:10.1016/j.jmaa.2014.12.056]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/142194
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