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<p>We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue points. The studies yield convergence results and also a density result between function spaces. We provide examples which show sharpness of the main convergence theorem. These examples give additional information about the convergence in the norm also, namely the difference between the functions in this setting and continuous functions.</p>

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On Lebesgue Points and Measurability with Choquet Integrals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月5日

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  • Petteri Harjulehto,
  • Ritva Hurri-Syrjänen

摘要

We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue points. The studies yield convergence results and also a density result between function spaces. We provide examples which show sharpness of the main convergence theorem. These examples give additional information about the convergence in the norm also, namely the difference between the functions in this setting and continuous functions.