A sharp nonconvexity bound for partition ranges of vector measures with atoms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:235

Article

Allaart, PC

关键词: partition range;    optimal-partitioning;    convexity theorem;    vector measure;    vector atom;    Hausdorff-distance;    digraph;    tree;   

DOI  :  10.1006/jmaa.1999.6402

来源: Elsevier

【 摘 要 】

A sharp upper bound is given for the degree of nonconvexity of the partition range of a finite-dimensional vector measure, in terms of the maximum (one-dimensional) mass of the atoms of that measure. This upper bound improves on a bound of Hill and Tong (1989, Anal. Stat. 17, 1325-1334) by an order of magnitude root n. Its proof uses several ideas from graph theory, combinatorics, and convex geometry. Applications are given to optimal-partitioning and fair division problems. (C) 1999 Academic Press.

【 授权许可】

Free