On the concentration of measure and the L1-norm

JOURNAL OF APPROXIMATION THEORY

卷:175

Article

Malykhin, Yu. V.¹  Ryutin, K. S.² 

[1] Steklov Math Inst, Moscow 119991, Russia

[2] MSU, Fac Mech & Math, GSP 1, Moscow 119991, Russia

关键词: Concentration of measure;    L-1-approximation;    Minimal support;   

DOI  :  10.1016/j.jat.2013.07.011

来源: Elsevier

【 摘 要 】

We seek a function in an N-dimensional subspace of L-1 that attains a half (more generally, a given part) of its L-1-norm on a set of least possible measure. We prove that such a measure is asymptotically maximal when the space is spanned by independent standard normal variables. This answers a question of Y. Benyamini, A. Kroo, A. Pinkus. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free