On the Primitives of Some Bilinear Henstock-Stieltjes Integrable Functions

Abstract

Primitives play a key role in many significant results in Henstock integration. For instance, they are used to characterize absolute integrable functions. The controlled convergence theorem which is the best possible convergence theorem for the Henstock integral involves primitives. Bilinear Henstock-Stieltjes integral had been the subject of study in previous works of the authors. This paper investigates primitives of bilinear Henstock-Stieltjes integrable functions under certain conditions on the integrands and integerators. It is known that in the case of bilinear Stieltjes integrals, a primitive, up to some extent, is influenced by its integrator. Interestingly, it has been known that unlike in the real and ordinary case, a primitive is not necessarily continuous.