Abstract
In 1998, Garces, Lee, and Zhao defined the so-called H 1-integral [I.J.L. Garces, P.Y. Lee, and D. Zhao, Moore–Smith limits and the Henstock integral, Real Anal. Exch., 24(1):447–456, 1998/99]. Later on, a full characterization of H 1-integrable functions was given by Maliszewski and the author [A. Maliszewski and P. Sworowski, A characterization of H 1-integrable functions, Real Anal. Exch., 28(1):93–104, 2002/03]. The characterization is in terms of generalized continuity and so is similar to the classical Lebesgue theorem on Riemann integrands. The present paper contributes to the theory with some results of this type for H 1-integral defined with respect to differential bases: namely, the McShane basis, path bases, and so-called free point bases. In the latter two cases, the characterization is partial (necessity condition being provided only).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
