Duality gap function in infinite dimensional linear programming

The concept of duality gap function in infinite dimensional linear programming is considered in this paper. Basic properties of the function and two theorems on its behavior are obtained by using duality theorems with interior conditions. As illustrations for the results, we investigate the parametric versions of an example due to D. Gale and parametric linear programs on spaces of continuous functions. The notions of Riemann–Stieltjes integral and function of bounded variation have been shown to be very useful for our investigations.