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<p>In this paper, we introduce a new operator defined on the dual of a Banach space and obtain a characterization of the Riemann–Pettis integrability of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{weak}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>weak</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-continuous functions In addition, we establish the spaceability of the set of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textrm{weak}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>weak</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-continuous functions that are not weakly Riemann integrable.</p>

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Riemann–Pettis Integrability of Weak*-Continuous Functions

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Nisar A. Lone,
  • Arif Farooq Mir,
  • T. A. Chishti

摘要

In this paper, we introduce a new operator defined on the dual of a Banach space and obtain a characterization of the Riemann–Pettis integrability of \(\textrm{weak}^*\) weak ∗ -continuous functions In addition, we establish the spaceability of the set of \(\textrm{weak}^*\) weak ∗ -continuous functions that are not weakly Riemann integrable.