Discrepancy and the error in integration
type: Item
instance of: scholarly article
title: Discrepancy and the error in integration
zbMATH Open document ID: 1018.11039
author: R. Smith
published in: Monatshefte für Mathematik
publication date: 2002-09-10T00:00:00Z
review text: For two unit measures \(\mu,\nu\) on \(\mathbb R^n\) and a collection \(\mathcal B\) of Borel sets the discrepancy is defined as \(\sup\{|\mu(B)-\nu(B)|: B\in{\mathcal B}\}\). For functions \(f\) on \(\mathbb R^n\) estimates for \(|\int f d\mu-\int f d\nu|\) are given depending on the discrepancy of \(\mu\) and \(\nu\) and the modulus of continuity of the function \(f\) or its derivatives. These estimates of Koksma-Hlawka type are obtained by Haar wavelet analysis.
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1798905
zbMATH Keywords: discrepancy
zbMATH Keywords: wavelet
zbMATH Keywords: integration
MaRDI profile type: Publication
full work available at URL: s006050200037
OpenAlex ID: W2067871583
DOI: 10.1007/S006050200037
description: scientific article; zbMATH DE number 1798905