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<p>We prove several results concerning the discrepancy, tested on balls in the <i>d</i>-dimensional torus <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_1935_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {T}^{d}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>, between absolutely continuous measures and finite atomic measures.</p>

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Discrepancy and approximation of absolutely continuous measures with atomic measures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月12日

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  • Luca Brandolini,
  • Leonardo Colzani,
  • Giancarlo Travaglini

摘要

We prove several results concerning the discrepancy, tested on balls in the d-dimensional torus \(\mathbb {T}^{d}\) T d , between absolutely continuous measures and finite atomic measures.