Year: 2025
Type: article
Abstract: McShane integrals are generalized Riemann type integrals. In this paper, monotone convergence of ?-McShane integrable function is discussed. Further we introduce ?-equi-integrability, and ?-uniformly absolutely continuity on a complete metric space, endowed with a Radon measure ? and a family of cells that satisfies the Vitali covering theorem with respect to ?. We find several convergence theorems based on ?-equi-integrability, and ?-uniformly absolutely continuity. Finally, we establish a necessary and sufficient condition for the sequence of ?-McShane integrable functions to be ?-equi-integrable with respect to ?-uniformly absolutely continuity.
Source: Filomat
DOI: 10.2298/fil2506831k
Authors: Hemanta Kalita, Hemen Bharali, Puja Sarkar
Institutions: VIT Bhopal University, Assam Don Bosco University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413246716