Research introduces boundedness of Riesz potentials and maximal operators for non-measurable functions, suggesting new insights.
We introduce Riesz potentials for Lebesgue non-measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or extended now using integrals taken in the sense of Choquet with respect to Hausdorff content. Some earlier results also for maximal operators are considered, but now for Lebesgue non-measurable functions.
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Harjulehto et al. (2026) studied this question.
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