Lattice Points in Large Borel Sets and Successive Minima

被引：0
作者：
Iskander Aliev
Peter M. Gruber
机构：
[1] School of Mathematics,
[2] University of Edinburgh,undefined
[3] James Clerk Maxwell Building,undefined
[4] King's Buildings,undefined
[5] Mayfield Road,undefined
[6] Edinburgh EH9 3JZ,undefined
[7] Forschungsgruppe,undefined
[8] Konvexe und Diskrete Geometrie,undefined
[9] Technische Universitat Wien,undefined
[10] Wiedner Hauptstrass e 8-10/1046,undefined
[11] A-1040 Vienna,undefined
来源：
Discrete & Computational Geometry | 2006年 / 35卷
关键词：
Computational Mathematic; Volume Versus; Lattice Point; Independent Point; Baire Category;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let B be a Borel set in Ed with volume V(B) = ∞. It is shown that almost all lattices L in Ed contain infinitely many pairwise disjoint d-tuples, that is sets of d linearly independent points in B. A consequence of this result is the following: let S be a star body in Ed with V(S ) = ∞. Then for almost all lattices L in Ed the successive minima λ1(S,L),..., λd(S,L) of S with respect to L are 0. A corresponding result holds for most lattices in the Baire category sense. A tool for the latter result is the semi-continuity of the successive minima.
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收藏
页码：429 / 435
页数：6
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