Some Convergence Theorems of the PUL-Stieltjes Integral

The PUL integral is an integration process which uses the notion of partition of unity [3]. The definition of this integral is similar to the Gauge integral, which was defined by Kurzweil and Henstock. Also, it is equivalent to the Lebesgue integral in Euclidean n-dimensional Spaces. Boonpogkrong [1] discussed the Kurzweil-Henstock integral on manifolds. The PUL-Stieltjes integral, established by Flores and Benitez [2], is a generalization of the PUL Integral. In this paper, we present some Convergence Theorems for the PUL-Stieltjes integral. Notions on the equi-integrability of this integral is also presented in the paper.