Functional Covering Numbers
Functional Analysis
2017-04-25 v1
Abstract
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric inequalities on covering numbers, such as volume bounds, bounds connected with Hadwiger's conjecture, and inequalities about M-positions for geometric log-concave functions. In particular, we obtain strong versions of M-positions for geometric log-concave functions.
Cite
@article{arxiv.1704.06753,
title = {Functional Covering Numbers},
author = {Shiri Artstein-Avidan and Boaz A. Slomka},
journal= {arXiv preprint arXiv:1704.06753},
year = {2017}
}