Point distributions in compact metric spaces, II
Metric Geometry
2017-01-17 v1 Probability
Abstract
We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given (Theorem 1.1). We generalize Stolarsky's invariance principle to distance-invariant spaces (Theorem 2.1). For arbitrary metric spaces, we prove a probabilistic invariance principle (Theorem 3.1). Furthermore, we construct equal-measure partitions of general rectifiable compact metric spaces into parts of small average diameter (Theorem 4.1). This version of the paper will be published in Mathematika
Cite
@article{arxiv.1701.04007,
title = {Point distributions in compact metric spaces, II},
author = {M. M. Skriganov},
journal= {arXiv preprint arXiv:1701.04007},
year = {2017}
}