On Lebesgue points and measurability with Choquet integrals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912264317042688 |
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| author | Harjulehto, Petteri Hurri-Syrjänen, Ritva |
| author_facet | Harjulehto, Petteri Hurri-Syrjänen, Ritva |
| contents | 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 of the functions in this setting and continuous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Lebesgue points and measurability with Choquet integrals Harjulehto, Petteri Hurri-Syrjänen, Ritva Functional Analysis 28A25, 28A20, 42B25 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 of the functions in this setting and continuous functions. |
| title | On Lebesgue points and measurability with Choquet integrals |
| topic | Functional Analysis 28A25, 28A20, 42B25 |
| url | https://arxiv.org/abs/2502.03267 |