ABSTRACT. Based on the McShane integral, we define the ????????−Stieltjes integral for real-valued function. In this paper, we will need the definition of an increasing function to bring the definition of the ???????? integral into the ????????−Stieltjes integral. The purpose of this paper is to define the ????????−Stieltjes integral as a generalization of the ???????? integral and investigate some of its basic properties such as uniqueness of the integral value, linearity, etc.
Keywords. McShane-Stieltjes integral, ????????-partition, ???????? integral, and increasing function