Bounds for alpha-Optimal Partitioning of a Measurable Space Based on Several Efficient Partitions
arXiv:1308.3504 · doi:10.1016/j.jmaa.2014.12.056
Abstract
We provide a two-sided inequality for the alpha-optimal partition value of a measurable space according to n nonatomic finite measures. The result extends and often improves Legut (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.
arXiv comment14 pages, 1 figure. This version contains a corrected proof of part (i) of Theorem 2