The classical McShane integral has been generalized by D.H. Fremlin  to the case of an arbitrary $\sigma$-finite outer regular quasi-Radon measure space. We present an alternate approach to the Fremlin integral for a non-atomic, finite quasi-Radon space.
"An Alternate Approach to the McShane Integral." Real Anal. Exchange 25 (2) 829 - 848, 1999/2000.