Abstract
The well-known Controlled Convergence Theorem[5] and the equi-integrability theorem[9] are the main convergence theorems of the Kurzweil-Henstock integral, which is of the non-absolute type. These theorems are fundamental in the application of the K H-integral to real and functional analysis. But their conditions can be weakened to extend their applications.In this paper, using the property of Locally-Small-Riemann-Sums[7], we give an other convergence theorem (Theorem 1). By Theorem 2 we prove that Theorem 1 contains the Equi-integrability Theorem and is not equivalent to it. Therefore the Controlled Convergence Theorem and the Equi-integrability Theorem are all corollaries of Theorem 1.
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.
