Search results for "generalized absolute continuity"

showing 2 items of 2 documents

THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL

2022

We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.

Settore MAT/05 - Analisi MatematicaHenstock-Kurzweil-type integralgeneralized absolute continuityDerivative in LrPerron-type integral
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On Descriptive Characterizations of an Integral Recovering a Function from Its $$L^r$$-Derivative

2022

The notion of Lr-variational measure generated by a function F ∈ Lr[a, b] is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the HKr -integral recovering a function from its Lr-derivative is given. It is shown that the class of functions generating absolutely continuous Lr-variational measure coincides with the class of ACGr -functions which was introduced earlier, and that both classes coincide with the class of the indefinite HKr-integrals under the assumption of Lr-differentiability almost everywhere of the functions consisting these classes

generalized absolute continuity of a functionHenstock–Kurzweil-type integralabsolutely continuous measureSettore MAT/05 - Analisi MatematicaGeneral MathematicsLr-derivativeLr-variational measure
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