On Riemann-type definition for the wide Denjoy integral
Adjoint classes of functions in the sense
Using the concept of the -integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.
Some Kurzweil-Henstock-type integrals and the wide Denjoy integral
Kurzweil-Henstock integrals related to local systems and the wide Denjoy integral are discussed in the frame of their comparability and compatibility.
The AP-Denjoy and AP-Henstock integrals revisited
The note is related to a recently published paper J. M. Park, J. J. Oh, C.-G. Park, D. H. Lee: The AP-Denjoy and AP-Henstock integrals. Czech. Math. J. 57 (2007), 689–696, which concerns a descriptive characterization of the approximate Kurzweil-Henstock integral. We bring to attention known results which are stronger than those contained in the aforementioned work. We show that some of them can be formulated in terms of a derivation basis defined by a local system of which the approximate basis...
On McShane-type integrals with respect to some derivation bases
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in is given.
Page 1