Approximation of discrete measures by finite point sets
type: Item
instance of: scholarly article
title: Approximation of discrete measures by finite point sets
arXiv ID: 2202.01501
publication date: 2023-08-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/2202.01501
review text: The author proves that for any discrete measure \(\mu\) on \([0,1],\) which is not supported on one point only, the best possible order of approximation in terms of the star-discrepancy is for infinitely many \(N\) bounded from below by \(1\slash cN\) for some constant \(6\geq c > 2\), which depends on the measure.
reviewed by: Roman Urban
Mathematics Subject Classification ID: 11K36
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 11J71
Mathematics Subject Classification ID: 11K31
zbMATH DE Number: 7726922
zbMATH Keywords: star-discrepancy
zbMATH Keywords: discrete measures
zbMATH Keywords: Borel measures
MaRDI profile type: Publication
cites work: Tusnády's problem, the transference principle, and non-uniform QMC sampling
cites work: Families of well approximable measures
cites work: Q4064235
cites work: Q4767350
cites work: Q4843175
cites work: Q4003879
cites work: Norm form equations
DOI: 10.2478/UDT-2023-0003
published in: Uniform distribution theory
Recommended article: Discrete approximations of continuous and mixed measures on a compact interval
Recommended article: Approximation by finitely supported measures
Recommended article: Discrete approximations of metric measure spaces of controlled geometry
Recommended article: On approximation of measures by their finite-dimensional images
Recommended article: Low-discrepancy point sets for non-uniform measures
Recommended article: Approximation by pointwise bounded sets of continuous functions
Recommended article: Q5387006
Recommended article: Discrete approximation theory
Recommended article: Q5170503
description: scientific article; zbMATH DE number 7726922