Discrepancy and the error in integration
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.
scientific article; zbMATH DE number 1798905