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<p>We prove the lineability of the set of Riemann integrable functions which are not measurable for certain Banach spaces. We also prove that, for a non-Schur space, the set of scalarly Riemann integrable functions which are not Darboux integrable is lineable.</p>

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On the Lineability of non-measurable Riemann integrable functions

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • T. A. Chishti,
  • A. F. Mir,
  • N. A. Lone

摘要

We prove the lineability of the set of Riemann integrable functions which are not measurable for certain Banach spaces. We also prove that, for a non-Schur space, the set of scalarly Riemann integrable functions which are not Darboux integrable is lineable.