On Lebesgue Points and Measurability with Choquet Integrals
Petteri Harjulehto, Ritva Hurri-Syrjänen · Journal of Geometric Analysis · 2026
Abstract 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.