On convergence of McShane type integral and Radon measure

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.