Search results for "Henstock Integral"
showing 3 items of 33 documents
A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure
2019
Abstract We introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil–Henstock-type integral related to this basis. We prove a version of Hake’s theorem in terms of a variational measure.
On Variational Measures Related to Some Bases
2000
Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.
Product local system and Fubini and Tonelli theorems
2008
We present an integral, called S-integral, de ned by means of Riemann sums related to product local systems on the plane. The classical Henstock integral on the plane with respect to the Kurzweil basis is an example of integral related to a product local system. Some properties and a Fubini type theorem for the S-integral are considered. A monotone convergence theorem for the integral constructed by a local sys- tem in the real line is given and it is used to obtain a Tonelli type theorem for a product local system.