Abstract
In this paper, we introduce the concept of strongly order continuity of a set function, and use it to investigate the convergence of measurable functions sequence and of integral sequence on fuzzy measure space. Several equivalent conditions of strongly order continuity are presented. It is shown that a necessary and sufficient condition that Lebesgue's theorem remains valid for a monotone set function is that the set function possesses strongly order continuity.
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.
