Proves that Lusin-type class functions are almost everywhere differentiable, indicating a new perspective on HK_r-integral.
It is proved that any function of a Lusin-type class, the class of ACGᵣ-functions, is differentiable almost everywhere in the sense of a derivative defined in the space Lʳ, 1≤ r<∞. This leads to a full descriptive characterization of a Henstock-Kurzweil-type integral, the HKᵣ-integral, which serves to recover functions from their Lʳ-derivatives. The class ACGᵣ is compared with the classical Lusin class ACG, and it is shown that continuous ACG-functions can fail to be Lʳ-differentiable almost everywhere. Bibliography: 20 titles.
No takes yet. Share an insight, caveat, or question.
Musial et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: