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<p>We develop a version of the Kurzweil–Stieltjes integral on compact lines and establish its fundamental properties. For sufficiently regular integrators, we obtain convergence theorems and establish a relationship to the Lebesgue integral with respect to positive Radon measures. Additionally, we introduce a notion of differentiation on compact lines which, when paired with the proposed integral, yields a formulation of the Fundamental Theorem of Calculus in this context.</p>

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Kurzweil–Stieltjes integration on compact lines

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Leandro Candido,
  • Pedro L. Kaufmann

摘要

We develop a version of the Kurzweil–Stieltjes integral on compact lines and establish its fundamental properties. For sufficiently regular integrators, we obtain convergence theorems and establish a relationship to the Lebesgue integral with respect to positive Radon measures. Additionally, we introduce a notion of differentiation on compact lines which, when paired with the proposed integral, yields a formulation of the Fundamental Theorem of Calculus in this context.